SWIG targeted for AllegroCL will generate wrappers specific to Allegro's proprietary FFI and will not be usable on other lisp implementations. Otherwise, SWIG for common-lisp can generate wrappers targeted to CFFI, which serves as a compatibility layer for all of the foreign interfaces of lisps that it supports. As such, however, CFFI tends to be something of a "least common denominator" among supported lisps and likely the SWIG generation will not be as comprehensive.
My understanding is that there is not much that can be done to interoperate fully between C++ and Common-Lisp. I'm aware of some experimental branches of ECL which sought to do so which claimed some degree of success, but I do not believe these reached the point of public release. At the very least, if you were to go that route, you'd be running on a lisp platform with very, very limited support.
There is another option you may wish to look into for generation of C wrappers that may give more comprehensive results, but that targets CLANG and LLVM compiler environment. If that is acceptable, you can have a look on github at the following two projects:
I'm sure I haven't given the answer you may have been wishing for, but I hope it can be of at least some help.