Bottleneck is probably combo of your CPU, [what video?] and motherboard chipset. [southbridge/northbridge which effects it all]
I'd try upgrading the chipset drivers and BIOS of your motherboard, found on your motherboard's web site, FIRST.
That CPU is a bit low for gaming, LoL is probably well optimized code and lower requirements as a result.
Not knowing all your hardware.... Fill in the specs, you can run msinfo32.exe from Start | search box and get the info there. Video card will be listed under Components | Display.
Guessing without it, that you could use a video card
and CPU upgrade, that CPU is circa 4Q/'07 so it has seen better days, whole system replacement is probably in order, to catch up to 2013 gaming.
Looking on newegg just for an idea, this is the only LGA775 slot CPU (same slot type as a E4600) even available, and it's a refurb: (plus no guarantee your motherboard supports it, without looking it up.)
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116903&IsVirtualParent=1
If your motherboard even has a PCI Express x16 slot, what version is it, 1.0/1.1/2.0? will likely limit a video card choice, also, let alone the PSU in it.