I seriously doubt if Clenzoil contains any solvents "hot" enough to lift or dissolve lacquer. I have used Clenzoil in the past and don't recall any strong solvent smells like toluene or MEK. While that is certainly not definitive proof, the smell test is commonly used in organic chemistry labs as a starting point for identifying unknown samples. At least it was when I was tasked with identifying unknowns in college organic chem lab classes.
If you do not get a reply from the manufacturer, you could Google search the MSDS. And you could also just spray a coat of the lacquer you use on a scrap piece of steel, let it set for a week or so, and then apply a healthy dose of Clenzoil to see if the lacquer begins to soften or lift. If it won't damage a fully hardened fresh coat, it is very unlikely to damage an old coat.
However, from reading a number of tests over the years to determine which gun oils provide the best protection, I do not recall any where Clenzoil was ever near the top of the heap. I found it OK for general use, but then again, I was not exposing my guns to weeks of continual salt spray and rain on the Alaska Peninsula either. What you should choose depends upon whether you are after long term storage, general rust prevention and lubrication, extreme conditions, etc.
