Lexington is very safe, but some of the roughest parts are around downtown. The opera house is just off broadway, and very near where I went to college, and that area is pretty heavily patrolled. As always, be aware of your surroundings, but don't let folks here scare you about that part of town. It's no more dangerous than any other spot in town.
I can't speak for policies at the Opera House, but in Kentucky, the prohibition against concealed carry on private property is considered a "policy", and does not carry weight of law UNLESS the property owner or staff ask you to leave. You then must leave, or you will be guilty of trespassing and charged under that statute. It is prohibited by law in some areas, like courthouses.
As a side note, I do not "walk past" NO GUNS signs in Kentucky because I respect the rights of private property owners to control their property. If I disagree with their stance, I don't violate their intrinsic rights, I just refuse to give them my money.