Beta-1,3-N-acetylglucosaminyltransferase that plays a key role in the synthesis of lacto- or neolacto-series carbohydrate chains on glycolipids, notably by participating in biosynthesis of HNK-1 and Lewis X carbohydrate structures. Has strong activity toward lactosylceramide (LacCer) and neolactotetraosylceramide (nLc(4)Cer; paragloboside), resulting in the synthesis of Lc(3)Cer and neolactopentaosylceramide (nLc(5)Cer), respectively. Probably plays a central role in regulating neolacto-series glycolipid synthesis during embryonic development. 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.