WAKEFIELD, N.H. — A Massachusetts family of four were found dead on Christmas Day at their lake house in New Hampshire after their propane heating system appeared to have malfunctioned, poisoning them with carbon monoxide gas overnight, authorities said Friday.

Matthew Goldstein, 52, was an elementary school teacher in Chestnut Hill and his wife Lyla Goldstein, 54, was a project manager at Microsoft. Their daughters, Valerie, 22, who was also a teacher, and Violet, 19, a college student,…