Two-dimensional lattice structures formed by racemic tartaric acid on a single crystalline Cu(110) surface have been studied and compared with the enantiopure lattices. At low coverage, the doubly deprotonated bitartrate species is separated into two-dimensional conglomerates showing opposite enantiomorphism. At higher coverage, however, a singly deprotonated monotartrate species forms a heterochiral, racemic crystal lattice. While the enantioseparated bitartrate system undergoes decomposition at the same temperature as the enantiopure system, the racemic monotartrate lattice has a lower thermal stability than the enantiopure lattice of identical periodicity and surface density. At monolayer saturation coverage, the pure enantiomers form a denser lattice than the racemate. This is in contrast to the three-dimensional tartaric acid crystals, where the racemate crystallizes in a lattice of higher density, which is also more thermally stable than the enantiopure tartaric acid crystals.