Beta-1,3-N-acetylglucosaminyltransferase that plays a key role in the synthesis of lacto- or neolacto-series carbohydrate chains on glycolipids. a beta-D-Gal-(1->4)-beta-D-Glc-(1<->1)-Cer(d18:1(4E)) + UDP-N-acetyl-alpha-D-glucosamine = a beta-D-GlcNAc-(1->3)-beta-D-Gal-(1->4)-beta-D-Glc-(1<->1)-Cer(d18:1(4E)) + H(+) + UDP a neolactoside nLc4Cer(d18:1(4E)) + UDP-N-acetyl-alpha-D-glucosamine = a neolactoside IV(3)-beta-GlcNAc-nLc4Cer(d18:1(4E)) + H(+) + UDP Protein modification; protein glycosylation. Belongs to the glycosyltransferase 31 family. Truncated N-terminus.