This should work out just fine. The LC2I has 2 Channels on INPUT but has 4 Channels of OUTPUT. You will get a Bass Output and a Main Output. It would be perfect if you’re tapping into a full range signal. This would give you all the frequencies you need to drive the system. Usually the front or rear will be full range unless it’s a multi-channel system with active crossovers controlled by the factory amp. Since you have a Bose system you might have a full range signal but I’m not exactly sure. You’ll want to tap into whatever signal has the widest frequency range.
i decided to use my powerbass asa 700.5 amp
do a 3 channel stage - front comps morel Maximo 6.5 and a single jl audio 10w3v3 2ohms ported.
that's going to my temporary set up
my real set up will be the pioneer 720prs and sealed single jl audio 12w6v2 powered by jl audio 300/2 or 300/4 and 250/1.
recently purchased a used arc audio xxd 4080 amp for a great price.