I might be an example of genetic mosiacism. At some point in the early embryonic life of the lobster, one of the dividing cells did not equally distribute its genetic material between the two daughter cells. As each cell line would go on to develop into different parts of the body, which would all exhibit the genetics of their ancestor cell, you end up with various odd effects. In humans, some cases of heterochromia iridium are due to mosaicism.
Imagine a lobster embryo at the two cell stage. as each cell divides, one does so successfully, the other unequally. The result is that three of the cells now have sufficient genetic material to express all characteristics of the lobster, and one is missing some. Two of those cells go on to form the anterior end of the animal, its cephalothorax, antennae and mandibles, while the other two go on to form the posterior end, including the tail and (crucially) the ventral appendages including the claws. If the deficient cell was one of this latter pair, you would indeed see half of the lower body differing from the other half, while the upper body was uniform.
That said, the cells of such an early embryo do not have such a well-defined future this stage. What normally happens is that the cells divide several times to form a small ball of cells, which then begin to exhibit distinct behaviours depending on what there future role is to be. Also it would be remarkable for mosaicism to be exhibited with such a high level of symmetry as there is no biological reason why all the deficient cells should end up on one side of the growing embryo and all the superficient cells on the other.