For video card issues, in addition to reinstalling the driver you want to try rolling back to a previous one or updating to a beta driver (if possible). The current version may be the issue, so you do those just in case.
Third party applications may also be the issue. Lolreplay was known to cause crashes in the loading screen for a time, for example. It's hard to pinpoint the issue if it doesn't happen every game, but things like overlays and recorders are particularly susceptible to doing this so it's good to try uninstall/disabling or reinstalling them. It's not often, but audio drivers can result in game crashes as well.
You can post over on the Help & Support board, but visiting the Wrenchmen (and other volunteers) at the League Community Discord is a great way to get help from those more knowledgeable than me.