Does LY comp status?
 

I'm Plat on CO, fly to Israel 3-4x a year.... do they comp status?

Very rare...if not never! To be honest if you fly 3/4 x a year you can gain status very quickly within EL AL specially on C/F fares. Also to get you off the mark you can purchase "King David Membership" which will cost you $300 but will enable you to check in Business/First Desk, give you use of the Lounge and Priority baggage.