I have been out of touch with actual development for some months, but back then, the Luck Stat was never considered in the likelyhood to find such an encounter.
You do understand how vague an answer this is right? Unless you're being gleefully cryptic in some hints...
Nothing of what you said puts any certainty into anything.
"back then"
Also no mention of PE check.
But now, is there a problem with my asking for this answer? If there is please tell me, and I'll of course stop asking. But as far as I know, the wiki aims to explain every detail of everything. I don't feel it's outlandish to want to know whether or LK or PE affect the chances.
And yes, I agree I would not look for an urban encounter in the dessert.