Livestock, like small goats and pigs, remain prohibited in urban Lexington’s backyards. A council committee this week rejected an exemption for those animals. Council Member Steve Kay sponsored the proposal.“I think we gave it a good shot. We may bring it back at some later time. But, I think for the moment, it’s off the table,” said Kay. Critics of an exemption for goats and pigs worry about waste, noise and enforcement. Council member Doug Martin believes the vast majority of Lexington’s residents don’t want pigs or goats living in their neighborhoods.