Ding!
Yes, there are acrylics that are not water, or even alcohol soluble. Phil mentioned methyl methacrylate, which is one of many, and more are being developed on a nearly daily basis.
I haven't used the paints in question, so I'm not familiar with the system. Since acrylics polymerize and therefore cure, it is unlikely that they are true lacquers—but organic chemists, particularly those who deal with coatings, are ingenious and inventive critturs. I can certainly see that an acrylic that behaves in some ways like a lacquer might be possible.
However, solvent compatibility in this case is particularly problematic because "lacquer thinner" is not a specific composition. Some of them are mostly alcohol, others contain substantial amount of much more aggressive hydrocarbons.
The best thing to do when not using the proprietary thinner is to test the compatibility. Make a mixture of the paint in question with the solvent in question, half of each. Store this in a tightly sealed glass bottle (as close to the volume of test solution as possible) overnight. If the stuff looks all right the next day, apply it to a clean styrene surface. Allow to cure overnight. If adhesion, finish, and color are as they should be, then the combination is at least marginally compatible. Full compatibility is indicated by stability over a period of not less than thirty days. I doubt anybody wants to wait that long.