I will lust you for the rest of my life
We definitely do not use" lust" in this way.
In formal English, we have "the lust of the flesh, the lust of the eyes, and the boastful pride of life." "Lust" is a noun there, though.
Typically, you lust after someone. It sounds very religious. I can't remember the last time I ever said that. Normally, you would say "Dang, they look good" instead of "Verily, I do lust after her in my heart."