it sounds like you have the
LG CM4550 or similar, and your connections to the speakers and sub looks something like
this
as americanaudiophile mentioned, it is probably best to disassemble that sub and take a look inside to be sure if it's passive or not (probably so)
If it is passive, that is a high-level output. I would trace that cable to the speaker and get the proper +/- labeled for phase and use that as your new "LFE" output. The line converter (something like
this) and use the + on the sub for the L and R input on the converter then use the RCA outputs to connect to your new sub amp.
How you wire up the amp depends on what amp you have and how many subs you have, I am using a mono sub amp with a dual-coil passive sub wired in series to get 8-ohm load and using an old 300W PC power supply to get about 200W of +12v into the amp. works very well with my Onkyo 65W/channel 5.1 AVR (the LFE output is input to my sub amp).