When we talk about "surrender" in the first step, it doesn't mean "falling", at all.
Those who surrender do not act out. They never do. It makes one free of the lust because we get out of Hashem's way and allow Him - yes, allow Him - to remove it. At least temporarily. It is in surrendering that we let go of the lust "opportunity". The surrender (or "giving up") is of two things simultaneously:
1 - the lust opportunity
and
2 - the need to overcome the overwhelming desire.
Those who think that "giving up" has anything whatsoever to do with giving in to the temptation have never done it themselves yet, and have not yet tasted this derech of recovery.