If he's playing at 1080p (which I suspect he is, if he was going 1440p or 4k he'd probably know the answer to his question as it's a bit more techy-territory) then almost anything will do those games fine. LoL can probably run on a calculator and CSGO runs on an engine which went in two by two in to the ark so anything modern will do.
Let's focus on LoL as it's the more demanding of those two games. A GTX 750ti (NOT the 750. Must be Ti) will probably hit 60fps at 1080p with everything maxed out. So will an R7 270 if AMD is your flavour.
Personally I'd go for a GTX 960 at minimum, or an R9 380 as these will also run other games well enough to be playable. Of course the sky is the limit and he can always crossfire a pair of 980tis to play 500 instances of LoL at the same time, all maxed out in 4k and still get 300FPS on each one, but that's overkill.
Keep in mind that if it's a used PC, that modular PSU might not have come with all the cables so he may have to replace one or two to power the GPU. A 750Ti doesn't need external power however, so if he goes with that, it's plug & play.
This is a good read.
http://www.logicalincrements.com/games/lol/