Can a monitor cause lag?

Input lag is an inevitable nature of all devices. For monitors, the tasks of their chips to process signals, adjust the contrast and saturation of the graphic and scale the image to proper size for the display panel, are the main cause of input lag.

Can an old monitor affect fps?

Sometimes, Old Monitor can also cause huge drop in fps while playing games. Upgrade Your monitor to 144hz and make sure that the cable you are using to connect is from good quality.