We consider the design of lattice vector quantizers for the problem of coding Gaussian sources with uncoded side information available only at the decoder. The design of such quantizers can be reduced to the problem of finding an appropriate sublattice of a given lattice codebook. We study the performance of the resulting quantizers in the limit as the encoding rate becomes high, and we evaluate these asymptotics for three lattices of interest: the hexagonal lattice A/sub 2/, the Gosset lattice E/sub 8/, and the Leech lattice /spl Lambda//sub 24/. We also verify these asymptotics numerically, via computer simulations based on the lattice A/sub 2/. Surprisingly, the lattice E/sub 8/ achieves the best performance of all cases considered.