League of Legends "Your Session Has Expired" is what many players have been seeing as they finished their games recently.
League of Legends Your Session Has Expired: How to Fix
After completing a game, many League players have reported that their log in sessions have expired, and are kicked from the game before they can honor other players. This is a problem in ranked queue; when players log back in, they're greeted with a penalty for leaving.
On the official server status page, Riot seems to be dealing with issues for other games as well. The session problems seem to be happening to everything on their client.
There isn't a fix you can do on your end, as the problem is on Riot's servers. Luckily, Riot is aware of the issue and have closed ranked servers in Europe. You'll just have to wait until the servers go back up, when the problem is hopefully fixed. To avoid incurring penalties, stay off ranked until it's fixed.