First, a lot is always two words. (There is a word allot but that's entirely different.
A lot of = many
Lots of = many, more informally
*A lots of = incorrect usage.
There were a lot of people there.
There sure were lots of peole there. - more informal
Why don't you try to write a sentence in which you're not sure whether to "although" or "though"?
Student or Learner