Is it correct to say "Lessons numbers one and two" or we should only use Lessons number one and two? 
 
If you want to study 2 lessons, then the above sentence is correct.
Today we will study lessons numbers 1 and 2. 
But I would actually leave out the word  �numbers � in this case.
 
If you are studying exercises number 1 and 2 in one lesson, the you would say 
Today we will study lesson 12, numbers 1 and 2 (or exercises 1 and 2).