This occurred mainly due to Stevenson endorsing Federal control of the Tidelands oil, while Eisenhower endorsed state control. LA Gov Robert Kennon, an anti-Long Democrat, endorsed Ike, as did a number of the more conservative LA Dems.
Still though, a double digit margin is a bit shocking
As I mentioned in my first post, Unpledged Electors received 7% of the vote that year, exaggerating the extent of Eisenhower's victory. Had that 7% gone to Stevenson, Eisenhower would have beaten him 53-47%, an almost exact reverse of the 1952 results in the state.