Well, I would tune your current system with a CD first. A genre you frequently listen to. I say this because iTunes is 1/10th the bit stream quality of a CD. iTunes, AAC and MP3s will sound muddy on just about any system. And Sirius is no better... the sound quality IMHO is terrible and I would not give satellite radio the time of day. I can't believe people subscribe to the service and surprised these guys are still in business. Sirius IMO is good for talk radio where quality really doesn't matter. Other than that, I wouldn't waste money on it. The stream is extremely compressed and much worse than AAC or MP3 files. Now, if you transfer your CDs to AAC or MP3 and they are lossless, then you'll get CD quality and they sound just fine on the standard LR4 system. I don't want to sound too harsh about these products, but they should not be used as benchmarks. A lot of consumers are truly fooled by them and complain when their auto systems sound like ass.
Now, although the standard HK system isn`t stellar in the LR4, it's not bad considering it's a base system and it definitely can perform better than any other standard system you'd get with a premium car. And you can find its sweet spot with some patience - and of course - if the system is new, it takes a little time to burn in.
There is a member on this board who upgraded his Lux system - and hopefully he'll chime in with suggestions. I'm sorry I don't remember his handle. One thing to remember though, the system won't easily hand-shake with mods... so I believe you pretty much need the entire setup from amp to speakers. HK systems are isolated IPs.