Catalysis of the reaction: beta-D-galactosyl-(1,4)-D-glucosylceramide + UDP-galactose = alpha-D-galactosyl-(1,4)-beta-D-galactosyl-(1,4)-D-glucosylceramide + UDP.
UDP-galactose:lactosylceramide 4II-alpha-D-galactosyltransferase activity