"A lot of apples" is correct, "lot of apples" is not. I think you meant "lots of apples", in that case there are no differences :). You can use them both with countable and uncountable nouns but I think "lots of" is more used and more colloquial.

You can't say 'lot of apples' without some kind of article. 'A lot' = many. 'Lot' is singular (describing a large group of 'things'), so it needs either 'a' or 'the' to be correct.