No, a life-long Democrat, as far as I can tell. If/when he voted Republican it was to vote against the Jim Crow Dems of the deep South. In his Nobel Peace Prize acceptance lecture, when he described the defeat of Goldwater in the preceding presidential election, he said that the US had rejected fascism and war. (LBJ was never nominated for a Peace Prize from anyone and MLK Jr would be protesting the Viet Nam war and Johnson when it turned out that "Asian boys would fight Asian wars if I am elected" was just campaign rhetoric.)