Oftentimes, (more so on ARAM), I see a lot of people wait a few seconds after taking damage, then attempt to suicide into turret for an execution. Almost half these times result in a free kill for the enemy team. So what's the correct amount of time?
After taking damage from another champion, 13 seconds must pass before being executed
Interestingly enough, some people actually don't realize that an execution still gives experience to nearby enemy champions, (but no gold).
Additional Facts to Consider:
While executions take 13 seconds without being damaged, when a player dies, all enemy champions who assisted in the last 10 seconds will receive assists (or the kill).
While short, hopefully this post has been useful to at least some of you. Happy holidays!