Mediates the transport of melibiose and other galactosides by a symport mechanism. Can use protons and lithium as coupling cations for cotransport, depending on the sugar substrate. It catalyzes proton-melibiose, lithium-lactose, and proton/lithium-methyl-1-thio-beta-D-galactopyranoside (TMG) cotransport. This protein seems to be lacking the ability to recognize sodium cations. H(+)(in) + melibiose(in) = H(+)(out) + melibiose(out) Belongs to the sodium:galactoside symporter (TC 2.A.2) family.