''Let's go over your assignment first'' = in this sentence, the usage of ''go over'' conveys the idea that the speaker is about to examine the person's assignment before doing something else. So, you should have in mind that 'go over' is used when you mean that you want to ''examine something'' or ''look at someone or something thoroughly''. For example: 1) ''The doctor will go over you in a minute.'' 2) ''Let's go over these papers, shall we?'' 3) ''No sooner had the teacher gone over the lesson than a student asked the same question.'' 4) ''I went over my whole room, yet I could not find my wallet!'' 5) ''May you go over those instructions again? I'm still a little confused!'' Hope that helps!

"Let's go over your assignment first" is grammatically correct. It delivers a meaning to go through/examine one's assignment before doing something else. In this case, "go over" has the synonyms of study/scrutinize/examine/look at etc. something. If you want to know more of these words' usage, you could type "Go over meaning" in google search bar. It'll help you to understand.