Riot games use TCP/HTTPS for client updates and login, and UDP for in-game data. On top of that, kernel-level protection components such as Vanguard are sensitive to software that interferes with the network layer. These two facts define the limits of proxy use.
The Client's Network Layers
A proxy can only affect the first two arrows. The bottom two arrows, which determine your gameplay experience, go direct.
Region Choice Determines Ping
Riot ties your account to a region (TR, EUW, EUNE…). A region change can only be made with the official transfer tool, and it moves the account's data. Changing your IP does not change your region; it only lengthens your connection route.
The fix for high ping in the wrong region is a region transfer, not a proxy.
Anti-Cheat and Network Software
Protection components that run at kernel level can conflict with drivers that route network traffic. Some VPN and tunnelling software causes the game not to start or to throw an error. An HTTP/SOCKS proxy that runs in user space generally causes no problems — because the game does not use it anyway.
Real Ping Troubleshooting
The items marked in red are the two practices that are mistaken for a solution and end up making the problem worse.
Where a Proxy Is Useful
In the Riot ecosystem, proxies are used for work such as esports analysis and market research: collecting different regions' store content, event calendars and the statistics published on the website. For this kind of data work, web scraping proxy infrastructure is a good fit.
To measure your latency you can use ping test tool, and to see your connection's exit point you can use the My IP Address page.