I'm surprised that no one has mentioned the new birth yet. The lost person is literally unable to stop his sin until he is born again. It's useless to say to him, "Yes, you have to give up sleeping with your girlfriend after you get saved." He can't comprehend the answer because he is dead in tresspasses and sins.
The excellent textbook by J. C. Macaulay and Robert H. Belton, Personal Evangelism, gives this advice for such a case in Ch. 20, "Miscellaneous Objections" (pp. 187-188):
A. “I CANNOT GIVE UP MY SIN.”
1. Ask Him Whether He Wants to Be Free from Sin.
Ask the person who has given this as a reason why he cannot come to Christ, if he really wants to be free from his sinful habits. Jesus said: “Men loved darkness rather than light because their deeds were evil.” He also said: “And ye will not come to me, that ye might have life.” Determine if the individual is desirous of living in his sin, or if he is in earnest about desiring to come to Christ but is under the impression he must free himself of sinful habits, which thing he knows he cannot do.
2. Show Him Christ Is Only Answer.
Agree with the fact that he cannot give up his sin, for the Lord Jesus Christ said: “Verily, verily, I say unto you, Whosoever committeth sin is the servant [slave] of sin.” A slave in Jesus’ day was never capable of setting himself free, he had to be freed by someone else. So Jesus continued: “If the Son therefore shall make you free, ye shall be free indeed.” He is very able to set the prisoner free, and He loves to do it.
3. Point Him to Christ.
If the person is sincerely seeking, point him to Christ who said He is able to set a person free. Remind him that Christ is now seated at the right hand of the Father, and that He is able to save to the uttermost all that draw nigh unto God by Him, because He ever liveth to make intercession for them.
4. Assure Him of New Life.
Another fact to give this one is that when one believes on the Lord Jesus Christ he becomes a new person, for the Bible says: “Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.” He receives a new life, he has a new destiny, a new spirit, even the Holy Spirit, comes in to dwell in his heart. In Christ he has died to sin, and he is to reckon himself dead to sin but alive unto God through Jesus Christ our Lord,’ He now has a new indwelling power to enable him to give up his Sin.