You'll want to grab the harness from the LTZ, and if possible the front speakers, tweeters and A pillar covers as well. You could make your own harness if you had the necessary connectors but there's a lot of wiring for that amp and it will probably be quicker to take out and then install the LTZ harness.
I don't know for sure but you may also need the radio from the LTZ. The Bose system head units output line level signals, not speaker level, and the amp expects those. If your LT radio doesn't have line level outputs, hooking it up to the Bose amp will yield less than stellar results.