The only concern that I'm aware of with old chineys is flue gases seeping through joints into the home if you have a chimney on the inside of the house.
Unless there is a huge hole where the gasses are drafting into the house rather than out the top this can never happen. No gasses come out the barometric damper, because the chimney sucks it doesn't blow. A crack or missing brick will cut the draft some, but the only way CO will enter the house through an unlined chimney is if there is no draft or the top of the chimney is plugged, and in both of those cases you have a huge problem that needs immediate attention that a liner wouldn't have solved. The safety concern with an unlined chimney is it can't handle a chimney fire, your house will burn to the ground before you get it put out if it's sucking air through the cracks in the mortar.