Are you trying to open the legacy client from the executable in the League folder, or clicking the "Launch Legacy Client" button at the bottom of the client launcher? If it was from the launcher like you're supposed to, when you open up the old client try doing a client repair. If not, use the launcher.
P.S Riot, you're a fucking sellout. You sold out to Tencent.
Tencent already owned most of it before, nothing actually changed in regards to the game when they bought the rest. Rioters got some more benefits and that's about it.