Mark 1:4
4 John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.
Luke 3:3
3 And he came into all the country about Jordan, preaching the baptism of repentance for the remission of sins;
These parallel passages are used to teach that someone gets to Heaven, at least in part, based on if they have repented of their sins. Let's examine that claim.
Immediately, we can dismiss the idea that this is talking about a requirement of turning from one's sins in order to get to Heaven.
This is because avoiding sin is keeping the Law, as sin is defined by the Law (Romans 7:7: 1 John 3:4), and yet how well we keep the Law has no role to play in our justification (Galatians 3:11). This is covered more in this article, as well as many other places on this site, and so I won't retread all of that again here.
There are two primary views of these passages from a Free Grace perspective.
The first view, and the one that I favor, is that "repentance" in these passages refers to a turning from unbelief to belief in the coming Messiah, who John was preaching about. Therefore, one receives the "remission of sins" by faith, as is testified to elsewhere in Scripture:
Acts 10:43
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
Was John the Baptist a prophet? Absolutely - and the above verse bears witness to the fact that he was preaching the same thing that everyone before him was preaching - which our passages in question are examples of - that whoever believes in the Messiah will "receive remission of sins".
To this end, a little later in the passage in Mark, John explicitly connects repentance to belief:
Mark 1:15
15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
Since repent simply means "to turn", as is discussed in this article, and context determines what we are turning from, the above verse is an exhortation to turn and believe the Gospel - turn from unbelief.
This is also later seen when Christ, referring back to John, connects the Pharisees' failure to "repent" with their failure to "believe":
Matthew 21:32
32 For John came unto you in the way of righteousness, and ye believed him not: but the publicans and the harlots believed him: and ye, when ye had seen it, repented not afterward, that ye might believe him.
They didn't repent, because they didn't turn from their unbelief. They rejected the Messiah that was being preached to them.
And finally, in the book of Acts, looking back on what John the Baptist preached, the Apostle Paul says:
Acts 19:4
4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
Above, we once again see "repentance" connected to the command to believe, because John the Baptist was commanding them to turn from unbelief.
The second view on these passages from a Free Grace perspective is that the command to "repent" is both a command to believe and turn from sin, and that the mention of "the remission of sins" is primarily speaking about a temporal forgiveness both for the individuals, and the Jews as a nation.
In this view, the fact that John was preaching an imminent kingdom where the Messiah would be a physical king is stressed, which is valid, since John's entire purpose was to "make ready a people prepared for the Lord" (Luke 1:17), who was shortly about to appear. To this end, he preached about the Kingdom of Heaven being "at hand" (Matthew 3:2, Mark 1:15), that is to say, "right around the corner", and that the King ruling that kingdom is going to be ruling with a rod of iron (Matthew 3:12, Luke 3:17).
The "remission of sins", then, would be speaking about something like "fellowship forgiveness" - basically a pardon by the coming King - which is discussed more in this article, rather than the "eternal redemption" (Hebrews 9:12) secured by the sacrifice of Jesus Christ, and received by faith in Him (Acts 13:39).
Whichever view one adopts on these passages, the fact remains that the Lordship Salvation view is a Biblical impossibility. Turning from sins to some unspecified degree does not justify someone before God in the eternal sense - in whole or in part - and these passages do not teach that it does.