How is "Once Saved Always Saved" not a license to sin?
"Saved" means safe, and sinning is not safe.
Can a person abide in unrepentant sins like lying, lusting, and hating and still be saved if they do those sins the rest of their life and die?
The Bible says >
"And those who are Christ's have crucified the flesh with its passions and desires." (Galatians 5:24)
Also, in Hebrews 12:6-11, it says
"you illegitimate and not sons" if God is not correcting you; and the writer says what happens because of our Father succeeding in correcting us.
From Galatians 5:24 and Hebrews 12:6-11, then, I would say, no, you can not keep on sinning and spend eternity with Jesus.
Now, you have listed things "like lying, lusting, and hating".
Philippians 2:14-16 says,
"Do all things without complaining and disputing, that you may become blameless and harmless, children of God without fault in the midst of a crooked and perverse generation, among whom you shine as lights in the world, holding fast the word of life, so that I may rejoice in the day of Christ that I have not run in vain or labored in vain." (Philippians 2:14-16)
So, in writing to Christians, Paul says we need to stop our
"complaining and disputing", so that we can
"become blameless and harmless, children of God without fault in the midst of a crooked and perverse generation". There is no procrastination, here, to some next life, but we are told to do this, now . . . in this life > right
"in the midst of" this evil world's
"crooked and perverse generation". God commands this; so I would say God considers this to be a realistic expectation . . . since God in us is easily and breezily and beautifully able to change us to
"become blameless and harmless" and
"without fault". God's love has His own almighty power to cure our nature to become
"as He is" "in this world" (please see 1 John 4:17).
He saves us so we are safe and at home with Him, in this love (Romans 5:5, Colossians 3:15). But, I personally understand, we always will need more correction and curing, while in this life.
Your list of "lying, lusting, and hating" has some of the more well-known sins; however, people can point at things like these, while not correcting their own sin problems which can be very destructive and deeply degrading.
"Complaining" is a sin which can work directly against relating intimately (1 Corinthians 6:17) and thankfully {Colossians 3:15, Ephesians 5:20) with God. God has executed people because of their complaining against how He provided for them > Numbers 21:4-6. And now we see how a number of people blaspheme God by complaining against and condemning His blessing of rain, and even in the public media ones call His blessing of rain "bad" weather. Certainly, God is not bad to provide us with rain which we so need for life on this planet.
And
"disputing" > arguing > is destructive and degrading against how God would have us relating in His love >
"submitting to one another in the fear of God." (Ephesians 5:21)
"swift to hear, slow to speak, slow to wrath" (in James 1:19)
"nor as being lords over those entrusted to you, but being examples to the flock." (1 Peter 5:3)
"with all lowliness and gentleness, with longsuffering, bearing with one another in love," (Ephesians 4:2)
"And be kind to one another, tenderhearted, forgiving one another, even as God in Christ forgave you." (Ephesians 4:32)
So, it can be easy to point at someone else's "lying, and lusting, and hating" which are more obvious sins; but we need, ourselves, to get our Father's correction of things like complaining and arguing . . . so we can get free from the evil spirit of disobedience (Ephesians 2:2) which has us disobeying God by arguing and complaining. Because Satan's spirit can keep us degraded so we do not find out how to love like the above scriptures say to love. The evil spirit of arguing and complaining is directly anti-God and anti-love; so we need to stop these things and learn how to love, with Jesus >
"'Take My yoke upon you and learn from Me, for I am gentle and lowly in heart, and you will find rest for your souls.'" (Matthew 11:29)