The Pentium 4405U and it's Intel HD 510 graphics core is actually not too terrible. Based on the benchmarks linked below from Notebookcheck.net it actually performs better than the Intel HD 4400. The benchmarks for the Intel HD 4400 are from laptop with a Core i5-4200u or Core i7-4600u.
I have actually have a laptop with a Core i5-4200u and the Intel HD 4400 graphic core (and a dedicated CRadeon HD 8850m GPU). I tested the intel HD 4400 in a few games and it was actually not too bad. With some tweaks to graphic settings I was actually able to play games at 1600x900 resolution with pretty decent performance. Playing at 1920x1080 definitely resulted with less than 25 FPS in most cases.
The games I tested are:
- The Elder Scrolls IV: Oblivion
- Fallout 3
- Mass Effect 2 & 3 (I am sure Mass Effect 1 works)
- The Elder Scrolls V: Skyrim
- Star Trek Online
If you are okay with purchasing a refurbished laptop and spending a little more money, then you can get a much better laptop than the one you are looking at. The following Acer laptop sells for approx. $388 CAD (excluding shipping); it has a Core i3-7100 and Intel HD 620 graphics core which is a pretty good increase in performance over the Pentium 4405u. The screen is 1366x768. You'll have no problems running LoL on ultra settings and gameplay should be smooth since the