"Lots of luck" is a common but very casual expression. We would not say "I wish you tremendous amounts of luck" -- that is grammatically correct, but does not sound natural. Other things you might hear an American English speaker say include "I wish you the best of luck" or "I wish you the best of luck in the world" or "I wish you the very best" (same wish for a great future/outcome, but without the emphasis on luck).