Can one relate the frequencies of vibrational modes within a molecule to the molecule's HOMO/LUMO energies?
No, I could not think of any relation between them. Orbital energies are solutions of the electronic Schrödinger equation, and as such, they describe the electronic state of a molecular system. Vibrational frequencies are solutions of the nuclear Schrödinger equation, and as such, they describe the nuclear state of a molecular system. The quantities that describe the electronic state are not related to the quantities that describe the nuclear one simply because they describe two different subsystems: the electronic and the nuclear one.
Note that usually we treat these two subsystems as being independent of each other (the Born-Oppenheimer approximation), but even if you go beyond that, what you'll see is that changes in the nuclear subsystem (say, changes in geometry during vibrations) might affect the electronic state. Consequently, molecular vibrations in principle can alter HOMO/LUMO (as well as any other orbital) energies, but I doubt this interdependence of electronic and nuclear states is the relation you're looking for.