Cut off and discard stem end from each chayote and slice the vegetable in half lengthwise. Remove seeds and use in another dish, if desired. If necessary, cut a thin slice off the rounded side of each half so it will sit level.
Place halves on a steamer rack set over simmering water, cover, and steam until crisp-tender, about 20 minutes. Remove from steamer and let stand until cool enough to handle. Using a spoon, scoop out the flesh from each squash half into a bowl, leaving a shell about 1/4 inch thick; reserve.
Mound the stuffing mixture into the reserved squash halves. Dot the tops with butter and place in a greased baking dish. Bake until the tops are golden brown, about 25 minutes.
Garnish with thyme sprigs and lemon wedges and serve piping hot.