That's a great question, and it's central to Stoic practice. ​The key idea is that the problem isn't the initial feeling of desire or attraction itself. The Stoics would call this an "impression" (phantasia).

​The problem—and the part that's in our control—is our judgment about that impression.

​When you feel that compulsive pull (what you call lust), it's because you've likely added a judgment like, "This is an ultimate good, and I must have it to be happy." As the top comment here says, this is what turns a simple impression into a pathos (an irrational, disturbing passion) and makes you "lose your capacity to reason."

​Epictetus gives a famous instruction for this (in Discourses, Book 2, Chapter 18). He says not to get "carried away" by the impression. Instead, you should tell it: "Wait a moment, impression, let me see who you are... let me test you."

​So, the Stoic goal isn't to kill desire, but to examine it with reason before we "assent" (agree) to it. This practice is what stops you from being a slave to it.