Client is stuck on loading

I checked on the Support page, and apparently your firewall or antivirus can prevent the client from changing its own files. I disabled Malwarebites and the issue was solved.

i had the same problem when trying to patch yesterday (28/6/2018), the patch never fully downloaded, tried restarting the patch several times (resulted in a restarting loop of the client) and tried hextech repair. The only thing that worked was to reinstall the entire thing. Needed to have the client patch over night since 1.3 gb of patch with 200mb/s resulted in a 500 minute eta. There have been a few posts about certain anti-virus (mostly avira) that gives a false positive on the new patch, so i recommend you reading those if your computer tells you that there is a trojan in your LoL files.