lots of / a lot of:
you can use these with plurals or with uncountable nouns, for example: a lot of apples / lots of apples, a lot of money, lots of money.
there is no difference in meaning, just be careful that you put 'a' before lot but when you use lots of, there's no 'a' before it.
a few / few:
you can only use these with plurals and NOT before uncountables (we use a little / little with those).
the difference in meaning is that if the speaker thinks that quantity is not enough, they say few without 'a'. for example: I just have few friends (they are not enough).
if you want to express small quantity but it's okay, use 'a few'. I have a few friends (meaning 3-4 but it's okay).