I recently got a 1991 Honda with 114,000. Transmission shifts hard. Had fluid changed at Aamco and they put in Lubegard. Can this damage transmission?

Likely, it won't do any damage but it does affect frictional characteristics. Lubegard makes fine products, which are often used to adjust frictional characteristics of the ATF to specific applications. Google the specific Lubegard product added, check it out, and ensure they added the correct product. Personally, I prefer to use Mobil 1 Synthetic ATF or Amsoil Universal Synthetic ATF, without adding any other additive, in automatic transmissions. I'd recommend you do the same. Civics don't have special needs and don't require Lubegard additives. In my opinion, it only increases the cost of maintenance and is not recommended by Honda.