Short answer
No. Jesus said so himself. Not every one who says to him "Lord, Lord" will enter the kingdom of heaven. Only the one who does the will of his Father will enter. He added that many who worked wonders in his name would be turned away with "I never knew you". In Luke he asks why people call him Lord and do not do what he says. When a man asked how to gain eternal life, Jesus told him to keep the commandments. So calling Jesus Lord does not save anyone. Jesus pointed people to the will of God (﷾), and so does Islam. The Qur'an asks for faith in the one God (﷾) and righteous deeds.
Full explanation
The verses Christians rely on
Paul, a Christian missionary of the first century, writes about being saved. Whoever confesses with his mouth the Lord Jesus, and believes in his heart that God (﷾) raised him from the dead, shall be saved. He adds that whoever calls on the name of the Lord shall be saved. Many Christians read these verses as a promise that accepting Jesus as Lord and saviour secures heaven.
“That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.”
“For whosoever shall call upon the name of the Lord shall be saved.”
What Jesus said about "Lord, Lord"
Jesus sets a different test. Not everyone who calls him Lord will enter the kingdom, only the one who does the will of his Father in heaven. Many will say they prophesied, cast out devils and did wonderful works in his name. He will tell them to depart. In Luke he asks why people call him Lord and do not do what he says.
“Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.”
“Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.”
“And why call ye me, Lord, Lord, and do not the things which I say?”
The will of the Father comes first
In the same breath Jesus puts his Father before himself. He does not name his own will as the test, but the will of his Father. He calls it his food to do the will of the one who sent him. He says he seeks not his own will. In Gethsemane he prays, not as I will, but as thou wilt. His family, he says, is whoever does the will of his Father. Peter, one of Jesus' disciples, says God (﷾) made Jesus Lord. A title God gives is not a claim to be God.
“Jesus saith unto them, My meat is to do the will of him that sent me, and to finish his work.”
“I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which hath sent me.”
“And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.”
“For whosoever shall do the will of my Father which is in heaven, the same is my brother, and sister, and mother.”
“Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.”
"Keep the commandments"
When a man asked what he must do to have eternal life, Jesus did not ask him to call him Lord. He told him to keep the commandments. Jesus also said that at his coming every man will be rewarded according to his works. The letter of James says that a man is justified by works, and not by faith only.
“And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life? And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments.”
“For the Son of man shall come in the glory of his Father with his angels; and then he shall reward every man according to his works.”
“Ye see then how that by works a man is justified, and not by faith only.”
What "Lord" meant
The Greek word kyrios, translated Lord, can mean 'sir', 'master' or God (﷾), and the context decides which. Servants used it to their master and disciples to their teacher. Mary Magdalene uses it to the man she takes for the gardener. The King James Version rightly translates it Sir. Jesus says his disciples call him Master and Lord.
Defines kyrios as one to whom a person or thing belongs and who has power over it: an owner or master. It is also a title of honour, used by servants to their master and by disciples to their teacher, before it is applied to God and to the Messiah.
“Jesus saith unto her, Woman, why weepest thou? whom seekest thou? She, supposing him to be the gardener, saith unto him, Sir, if thou have borne him hence, tell me where thou hast laid him, and I will take him away.”
“Ye call me Master and Lord: and ye say well; for so I am.”
What the Qur'an says
In the Qur'an Jesus tells his people that Allah (﷾) is his Lord and their Lord, and that they should worship Him. The Qur'an sets the same condition Jesus set. Whoever hopes to meet his Lord must do righteous deeds and join no partner in His worship. Man is in loss except those who believe and do righteous deeds.
“They do blaspheme who say: "Allah is Christ the son of Mary." But said Christ: "O Children of Israel! worship Allah, my Lord and your Lord." Whoever joins other gods with Allah,- Allah will forbid him the garden, and the Fire will be his abode. There will for the wrong-doers be no one to help.”
“"'It is Allah Who is my Lord and your Lord; then worship Him. This is a Way that is straight.'"”
“Say: "I am but a man like yourselves, (but) the inspiration has come to me, that your Allah is one Allah: whoever expects to meet his Lord, let him work righteousness, and, in the worship of his Lord, admit no one as partner.”
“By (the Token of) Time (through the ages), Verily Man is in loss, Except such as have Faith, and do righteous deeds, and (join together) in the mutual teaching of Truth, and of Patience and Constancy.”
Verse by verse
Romans 10:9 — Epistle to the Romans, chapter 10, verse 9
“That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.”
Cited for
Whoever confesses Jesus as Lord and believes that God raised him is saved. Salvation comes by faith, not by works.
The response
Jesus himself set a different test. Not everyone who says Lord, Lord will enter, but the one who does the will of his Father. Asked the way to eternal life, he said keep the commandments. The letter of James adds that a man is justified by works, and not by faith only.
Where it lands — In Jesus' own words, calling him Lord is not enough; he asks for doing the will of God (﷾).
Matthew 7:21 — Gospel of Matthew, chapter 7, verse 21
“Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.”
Cited for
Jesus is only warning against hypocrites whose faith is not real. Those with true faith are safe.
The response
These people call him Lord, Lord, the very confession Christians say saves. They also worked wonders in his name. Jesus does not ask whether their faith was real. He names one test, doing the will of his Father in heaven. They are turned away because their deeds were iniquity. In John, eternal life is to know "the only true God, and Jesus Christ, whom thou hast sent". Islam asks the same.
Where it lands — The dividing line Jesus draws is doing the will of his Father. Calling him Lord, or working wonders in his name, is not enough.
Romans 10:13 — Epistle to the Romans, chapter 10, verse 13
“For whosoever shall call upon the name of the Lord shall be saved.”
Cited for
Paul applies a verse of the prophet Joel about calling on the LORD to Jesus, so 'Lord' here means God.
The response
Four verses earlier, Paul says what must be believed: that God (﷾) raised him. Peter quotes the same verse of Joel. He then calls Jesus a man approved of God (﷾), whom God (﷾) made Lord. A Lord whom God (﷾) made is not the LORD of Joel.
Where it lands — Paul and Peter, who both quote Joel, place Jesus under God (﷾), who made him Lord. Jesus' own test for the kingdom is doing the Father's will.
Perspectives
Mainstream Christian
Salvation is by grace through faith in Jesus as Lord, not by works. Matthew 7:21 warns against an empty profession of faith: true faith shows itself in obedience.
Paul writes that whoever confesses Jesus as Lord and believes that God raised him from the dead shall be saved.
Rebuttal
Paul does write this. But Jesus himself set the test: not everyone who says Lord, Lord will enter, only the one who does the will of his Father. Asked the way to eternal life, he said keep the commandments.
Christians hold that salvation is a gift received by faith, not earned by works. They read Matthew 7:21 as a warning against false faith.
Rebuttal
Obedience does matter, as Christians say. But these people called him Lord and worked wonders in his name, and he still names one test: the will of his Father. Where John's Gospel makes that will belief in the Son, it is belief in "the only true God, and Jesus Christ, whom thou hast sent".
The Islamic perspective
Jesus made doing the will of God (﷾) the condition for entering the kingdom. Calling him Lord, and even working wonders in his name, is not enough. The Qur'an teaches the same: faith in the one God (﷾) and righteous deeds.
Jesus says that not everyone who calls him Lord will enter the kingdom of heaven. Only the one who does the will of his Father will enter.
Jesus says many who prophesied and worked wonders in his name will be turned away.
Asked how to gain eternal life, Jesus answered: keep the commandments.
Jesus put the will of the Father above his own will.
"Lord" (kyrios) was used for a master or teacher as well as for God (﷾). Acts says God (﷾) made Jesus Lord.
The Qur'an teaches that salvation belongs to those who believe in the one God (﷾) and do righteous deeds.