The Gillespie is probably a single component alkyd enamel. Putting anything 2K or lacquer based over it may cause problems depending on the age of the Gillespie.
A couple things you can do when faced with a reaction problem between paints:
Apply a sealer between the 2 products and apply the new paint relatively dry and use fast drying reducer.
Bulldog adhesion promoter is a great product that acts both as an adhesion promoter and a clear sealer. Apply 3 light to medium coats allowing it to flash 10 minutes between coats, then apply your basecoat and clear. Apply the basecoat in light, dry coats and allow to dry good before clearing.
Many paint manufacturers also sell 1K sealers that work too, but it seems no one offers a clear one anymore.
Epoxy primer/sealers are also pretty good at preventing lifting caused by dissimilar paints. You can mix it 2-1-1 and apply as a sealer, but be careful because the reducer (either acetone or urethane reducer) can cause lifting if applied too wet.
Last option would be a waterborne sealer, if all else fails.
Personally I'd try the bulldog adhesion promoter, it comes in an aerosol can as well as qts. It's got me out of similar situations several times. Only thing is, apply it in light coats, don't try to lay on a wet coat, and let it dry 1/2 hour before applying color.
