JL's VXi line all have integrated DSPs. Since you already have a sub amp, however, I would get an amp/dsp that allows you to output a corrected signal to another amp. Audison's Prima amps with DSP have that option, but I don't think they're the only game in town. That said, if you're never going to upgrade the front speakers, the LC2i Pro will be just fine for the sub - no need to spend big dollars for a DSP just to tweak a sub's signal, IMO. However, if you do ever plan to upgrade the front speakers, an amp/DSP combo will be very nice to have. It is a pretty slippery slope.
After your post I went back and looked at my Sony amp (haven't installed yet) and it has speaker level inputs (wire harness) and audio sensing which allows me to tap signal from front speakers going to amp. I do not need to install the LC2i. I didn't recognize my amp had this capability. I don't think I will ever upgrade door speakers as I am only looking for more base. Thanks again.
L2Ci does more than take speaker level inputs - it also provides signal correction. The stock system rolls off low frequencies which you'll want to "put back" via external EQ/DSP. The bass boost option on the amp might be enough to get by.
I didn't need much help from amp's bass boost as my speaker and enclosure satisfied my bass desire (lol). Thanks again.