There is no difference in meaning: lots of=a lot of. But it's incorrect to say "a lots of questions" or "lot of questions (without the "a")".

A... signifies singular so "a lot", historically the term "lot" comes from a collection of items in an auction." "Lots" plural is just that many lots historically but now just the plural of a collection of things/emotions etc Today, you can use them interchangeably with natives speakers and no one cares.