Catalyzes the transfer of galactose from UDP-alpha-D-galactose to lactosylceramide/beta-D-galactosyl-(1->4)-beta-D-glucosyl-(1<->1)-ceramide(d18:1(4E)) to produce globotriaosylceramide/globoside Gb3Cer (d18:1(4E)). Also able to transfer galactose to galactosylceramide/beta-D-Gal-(1<->1')-Cer. Globoside Gb3Cer is a glycosphingolipid of the globo serie, one of the major types of neutral root structures of glycosphingolipids, that constitute a significant portion of mammalian cell membranes. a beta-D-Gal-(1->4)-beta-D-Glc-(1<->1)-Cer(d18:1(4E)) + UDP-alpha-D-galactose = globoside Gb3Cer (d18:1(4E)) + H(+) + UDP beta-D-Gal-(1<->1')-Cer + UDP-alpha-D-galactose = alpha-D-Gal-(1->4)-beta-D-Gal-(1<->1')-Cer + H(+) + UDP Glycolipid biosynthesis. The conserved DXD motif is involved in enzyme activity. Belongs to the glycosyltransferase 32 family.