Meggan Arnoux, a chef who oversees the Lagunitas organic school lunch program, was doing early-morning prep work when the call came at 9:30 a.m. on a Wednesday in March. Her husband, Mario, had bad news: Their goats were dead.

Named after her father and uncle, Timmy and Jimmy, the Nigerian dwarf goats were neighborhood characters whose personalities bore a striking resemblance to their namesakes. Timmy was boisterous and outgoing; Jimmy was more reserved. Neighbors loved…