There is an exact time for going afk and being warned by leaverbuster, and then being booted for a game. I think it's about time I figure out what that time is exactly xD I'll test it in a custom game.
I've been punished by leaverbuster before without actually being booted from the game and only warned, but this might be because I was reported for afk by other players afterwards. I'm sure there is a system that flags you to be penalized by leaverbuster. It might be related to reports, or just going afk in general to engage a script.
Update #1: So after testing in a custom game, the exact time it takes for a warning message to appear is 3 minutes and 5 seconds. I'll pull some more tests on other details in a bit.
Update #2: Following the 3 minutes and 5 second mark, it takes an additional 2 minutes to be booted from a game. That means it takes 5 minutes and 5 seconds on inactivity to be booted from a game. We'll see what "inactivity" means. There might be ways to "stay active" be having an ability that costs mana toggled and refilled at base, simple clicks, etc.
Update #3: Moving the camera around, pressing okay on the leaverbuster warning notification, activating toggle abilities like Wukong Q or Karthus E, buying items, and/or putting points into abilities has absolutely no effect on stalling leaverbuster. It will still take 3 minutes and 5 seconds for the warning message to display, and 5 minutes and 5 seconds to be disconnected.
Update #4: After fiddling around with certain locations, I noticed the actual warning message appears after only 3 minutes, and the following boot will still happen in the next 2 minutes of being inactive. This is probably because being inactive is brought on hold the first 5 seconds of the game, before the gates open for you to leave the shop. While the gates don't last 5 seconds, I'm guessing Riot just decided the first 5 seconds shouldn't be penalized for some reason, maybe to make a partial phase to realize the game is going, and another phase to leave the gates in a timely fashion. Or maybe they want the first 5 seconds not to matter for connection reasons. Regardless of their reason, in the first 5 seconds of the game, you are always considered, "active". Also, your inactivity is pretty much based entirely on your clicking, not movement. This means that, theoretically, if your auto-pathing takes 5 minutes to get to your destination and you do not click anywhere else for 5 minutes, you will be disconnected from the game for inactivity. The only way to refresh inactivity timers is by clicking to move. For this reason I want to test dashes or damage on leaverbuster, because dashes are an alternate means of movement, and taking/dealing damage is more of a high profile action. It seems pretty interesting to travel the map by using abilities and slaying dragons or barons, yet still being recognized as afk because you didn't actually click anywhere.
Also on a side note I just realized... It takes 5 minutes to be disconnected from a match, and it also takes 5 minutes for a flash to come off cooldown. Summoner spells are not available for the first 13 seconds approximately. So, in the how to tip that says it takes a certain amount of time to flash from one fountain to the other, how the hell did Rito test this?