$400 pc for LoL
PCPartPicker part list: https://pcpartpicker.com/list/d8rQMZ
Price breakdown by merchant: https://pcpartpicker.com/list/d8rQMZ/by_merchant/
CPU: AMD - Ryzen 3 2200G 3.5GHz Quad-Core Processor ($99.57 @ Amazon)
Motherboard: ASRock - B450M PRO4 Micro ATX AM4 Motherboard ($79.74 @ Amazon)
Memory: Patriot - Viper 4 8GB (2 x 4GB) DDR4-3000 Memory ($71.99 @ Amazon)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive ($52.99 @ Amazon)
Case: Rosewill - FBM-01 MicroATX Mini Tower Case ($19.99 @ Amazon)
Power Supply: Corsair - CXM (2015) 450W 80+ Bronze Certified Semi-Modular ATX Power Supply ($46.99 @ Amazon)
Total: $371.27
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-10-31 18:27 EDT-0400
Here's what I came up with. It's a tried-and-true build setup that I used for my brother's PC. The case is up to you, because you still have some cash left over if you want to push for your budget.
My brother also plays League, he says he hits 60FPS on medium settings 1080p.

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