Will a 650 dollar pc work Minecraft withought any lag?

We do not know. Price alone does not determine performance.

Depends what hardware the PC contains. No way of knowing that based solely on price, update your question with a link to the specifications of the PC.

If a $50 computer has a $600 video card in it, no. If a $600 computer has a $50 video card in it, just maybe to no. Somewhere in between, probably.

Minecraft works on smartphones, even old pc can run minecraft

This is why i'm a console gamer.