This laptop has a great i7 CPU and a GTX 850M, which will definitely run LoL at high settings. It's slightly over your budget at $799. However, if you're fine with refurbished laptops, you can get the same laptop refurbished for a hundred dollars less:
For mid range gaming I would go for HP ENVY - 14t cost around $600. This has Intel(R) HD Graphics 5500 that could even run Battlefield 4 and would give 32 fps in middle settings and would surely won't have any problem playing LOL in higher settings.