The Los Angeles Kings have only picked first once in their franchise history, and that was all the way back in 1967, the first year they were in the NHL. However, there was another time in franchise history when they would have had a chance to pick first if not for league rules around the lottery.
In 1995, the NHL put in place a lottery for the non-playoff teams to determine the draft order. Whichever team finished with the worst record had the best odds and those odds diminished based on how they finished in the standings.