Question

2 oraciones con a lot of
2 oraciones con a lots of

Answer 1

A lots of no existe es simplemente lots of sin el a, cuidado que es un error común. También se puede decir a lot of, pero con lot en singular. 
1. There are lots of/a lot of books that I would like to read.
2.Lots of / a lot of people live in China.
3.I have to study lots of/a lot of subjects

Answer 2

LOT OF:
1) A lot of time is needed to learn a language. 
2) A lot of my friends think it is going to be a war.     

LOTS OF:
1) I like lots of other countries and lots of other people 
2) I wish you lots of luck.