Valve has announced a Left 4 Dead 2 beta for Linux is available. if you have paid copy you should see the beta in your steam library, if you can’t see simply restart steam and you should see the install option.
According to Valve:
“The Beta build not only allows Linux owners to play the game natively, it is also the testing ground for our new Extended Mutation System.”
It is not a limited version but give full version with authority tool and dedicated server beta. it also support 4 maps, City 17, Diescraper Redux, Back to School and UrbanFight.