Higher resolution can lower your fps of course, it depends on the power of your grahics card / computer.
A monitor by itself should not lower your FPS or give you lag.
You should check your graphics card info (online works), see what the maximun resolution it allows, then check what's the max resolution your laptop allows (the max allowed in windows). If you graphic cards supports a higher resolution you would benefit from getting a bigger monitor, because more resolution = better gameplay, specially in a fps.
However, your computer might not be able to handle it as good (it should if you have good FPS at 1300x) so your best bet I guess would be to test before buying, but that pretty much always applies.