Which one of the 'Aztec Grass' do you have?
Liriope muscari 'Aztec'
Ophiopogon jaburan
Both are know as Aztec Grass in the trade.
O. jaburan isn't hardy below 20°F (Zone 9), but a lot of nurseries in Zone 7 are selling it as a hardy perennial grass.
There once was a Landscape Designer on HGTV(back when the G designated Garden) that used it in every design in South FL.
L.muscari 'Aztec' is similar to 'Variegata' which is an extremely slow growing plant for me. I have divided clumps of it and it has required several years to grow into a decent sized clump again. I have never applied a high Nitrogen content fertilizer to it, which is probably what it needs, along with some Potassium(Potash) for root development.
Rb

I honestly don't know. I didn't realize there was more than one kind. I got it at Lowe's and it is very similar to liriope in size and habit, at least in the pot. The foliage is a soft almost grey green with white stripes in it. It's beautiful in my white border. I had two six inch pots of it and divided them into probably 30 or more little sprigs. The ones that survived the armadillos are probably three inch diameter clumps after only a year. My main concern is if it is invasive, and if so, how badly?

I don't believe either one would be invasive. Both are in the Lily Family and spreads by short rhizomes.
There may be some seedlings occasionally appear in the garden from wind/animal/bird dispersion, but are easily relocated or discarded, if they aren't variegated and you don't want them.
The flowers are much different on the 2 species. If you are curious as to which you have, you could google for images of the 2 plants.
BTW, there are documented cases of Ophiopogon jaburan surviving winters outdoors in Zone7, but no details available as to conditions of habitat(protection, microclimate, etc.)
Good gardening!