mvaughn25,
The Texas Government Code does not permit a governmental entity to legally post 30.06 and 30.07 signs on a building “owned or leased by a government entity.” So if the government owns the property, the government may not post no carry signs. Similarly, if the government leases the property, the government may not post the signs.
Unfortunately, when a private company leases the building and posts no carry signs, there is no law preventing the private lessee from doing so. This creates a kind-of loophole for private lessees on government owned property. The government may not post the signs, but the government can give the right to post signs to the private lessee in the lease contract. According to the Office of the Attorney General of Texas, as long as the government does not instruct the lessee to post 30.06 or 30.07 signs, the private lessee may legally post no carry signs. The signs will have the force of law.
Does school lose designation?
Unfortunately, school district property never ceases being classified as school district property. According to the Office of the Attorney General, this means you can never carry on property owned by a school district, regardless of who is leasing it.