It's in Protestant northern LA and it's adjacent to the Mississppi river valley which has a larger black population. I guess the parish is distant enough from them to attract whites who don't want to live there.
It is also interesting to point out Cameron Parish in the southwest corner of the state which I guess is more Catholic but has swung Republican much harder more recently while LaSalle Parish flipped in the 1950s.
That's arguably at least part of the reason. While LaSalle had already flipped to Eisenhower in 56 the Democrats nominating a Catholic certainly didn't help. As someone else pointed out further up thread it may have attracted Mississippi whites from the black belt, maybe fleeing to a Catholic majority state and being Protestants contributed to a higher then average level of southern white bigotry.
