Can you upgrade the grapics card on a Lenovo H50?

Probably so. Depends on slots available on motherboard, type of slot, physical space for card, and most important, power supply capacity. There are many models of "H50": http://www.amazon.com/...f4tbtekv_e
And Lenovo page does not tell what size is in any. Now up to you.

A 750ti is your best bet as your psi is probably your wealth spot