To wish luck "at" or "in"?
Solution 1:
You can follow good luck with a variety of expressions. You can also precede studies with a variety of expressions.
For example, a young man might be busy at his studies in the evenings. He may struggle with his studies, only to succeed in his studies after much hard work.
Generally speaking, if you can put a noun at the end of a phrase, you can put good luck in front of the phrase and have it make sense. If you want to sound “natural”, look at (or imagine) the spoken sentence that might have preceded the wishing of good luck.