A $250 laptop that can run modern games without lag or issues does not exist. Even if you are looking at used laptops.
The above recommend HP laptop by
borislav1212 for $260 has an AMD A6-7310 APU with a Radeon R4 (Beema) integrated GPU. The processor itself is not very powerful, and the Radeon R4 (Beema) is less powerful than the Intel HD 4000 graphics core that is in all 3rd generation "Ivy Bridge" Intel CPUs released in 2012. That's the performance you should expect in the $250 range.
The link below has game benchmarks for the Radeon R4 (Beema).
https
/www.notebookcheck.net/AMD-Radeon-R4-Beema.115399.0.html