“Let's just not bother cooking tonight.”
Last night, you had a party and you have a lot of leftover food. You don't want to cook tonight. You suggest this to your family.
Let's just not bother cooking tonight.
You use this phrase when the action you're describing seems easy, simple, fast, unimportant, or unexciting:
I just googled "new york florist" and that was the first shop that came up, so I called them.
A: What did you do this weekend?
B: I just sat at home and watched T.V.
When you want to suggest that people in a group not do something, you can say "let's not ___". For example:
Let's not go out tonight.
You can use "Let's not ___" when you're suggesting something that you're sure the listener will agree with. In the example above, you think that everyone will agree that it's a good idea not to cook.
The phrase "not bother ___ing" means to not do something that isn't needed. For example:
Don't bother washing those — I'll put them in the dish washer later.
I don't bother shaving on the weekend unless I have to go out to meet with someone.