In my opinion. The solution to this problem would be not being able to call a lifecheck if there are more than 5 Alive people showing on the Leaderboard and it should not be allowed to call a lifecheck without explaining it.

For example what should be allowed: Lifecheck! -Type something in the chat fast or else i will have to kill you!-
What should not be allowed: Lifecheck

About the Detectives... no. That's doesn't help. Because if someone is a Detective that doesn't mean that he is not able to call a lifecheck at the first seconds of the round and kill everyone who doesn't respond. Also innocents should be able to call a lifecheck because at the end of the round (when it's needed to check who is alive) most likely the Detective is going to be dead and the remaining innocents will have a problem knowing who is alive or not.