Catalysis of the transfer, in a beta 1,3 linkage, of D-glucuronic acid (GlcUA) from UDP-D-glucuronic acid to N-acetyllactosamine (galactosyl beta-1,4-N-acetylglucosamine).
galactosyl beta-1,4 N-acetylglucosamine beta-1,3 glucuronosyltransferase activity