Laptop under $250 that can run minecraft with no lag?

Laptops are not very good for gaming and you are asking for a cheap laptop too. If you want a laptop that will run games half way decent you are gonna have to spend at least $300, unless you are looking for a used one.

I think honestly you might struggle. The problem with Minecraft is that its requirements can scale hugely depending on what you're doing. Minecraft can crash full on gaming PCs if you do something crazy enough with it, so a laptop, particularly one bought on as tight a budget as that isn't going to be the best starting point. To avoid disappointment I'd suggest saving up for a little longer before you begin looking.