Best Home Theater Amp

I have only heard Piega speakers but owned Aerials - if you get the Aerials be sure to get a good high powered amp.
In the last two years I have moved from 2 channel to 5 channel (mainly for music, but I also use it for HT) and currently enjoy the Cary Cinema 5 amp. Before that I had the McIntosh MA6900 and before that the Rowland Concentra, both highly regarded integrateds. The Cary impresses me daily - I thought it would be a compromise but it has not been. Plus 200 w/ch - while I have relatively efficient speakers (90 dB/W claimed) it has never flinched, even when driving all 5 identical speakers. I think if I was buying Aerial though (depending on the model) I'd consider 2 of the amps, though that would really create quite a large cable budget!
One bit of advice going off topic - if I was considering any speaker line to go MCh, I'd get their smaller speakers (monitors or small floorstanders) and get a great sub. The bigger the speakers the harder they are to integrate into your room with a 5-7 channel set up, and the sub allows you to adapt the bottom end to the room while the high quality speakers handle the other frequencies well.

I have found a Sim Audio Titan amp to compete with the best of them for home theatre. It compares pretty favorabley with their W5 model. I used one in an Sim Audio setup. Very neutral sound with 200W/8 ohms and 400W/4 ohms. Plenty of power but a beast with the 5 channel model at over 100 lbs. Make sure you have the room for it

Yes, this is an incomplete question! It's like asking, "what is the best car part?", or "what is the best ingredient in a recipie". It's all dependent on the rest of the team, and personal preference, even system matching.
One "perfect" amp for one system might not be even a workable choice for another.

I am very happy with my Classe CAV 500. Less than 5000$ on audiogon. Rated conservatively at 200wpc all channels driven. It is a 5 channel amp. RCA and Balanced. A lot better than my Sunfire cinema grand with similiar power ratings.

I would recommend the Proceed Hpa 2-3 They are both an audio bargin due to proceed going out of business.

I currently have the Piega P4 series of speakers, but I am looking for an amp that can carry me through for a number of years and handle my next speaker purchase (likely Revel or Aerial)

What speakers are you using? That might help us to provide you with better suggestions. Also, any particular reason you feel the need to upgrade from the Lexicon - not enough power, not the sound you like, etc.?? Any interest in the LX series?

Anthem is one worth looking at. Their P5 and P2 (5-channel and 2-channel) are 325w/ch and should provide more power than you'll need unless you have very power hungry speakers. They also have the A5 and A2, but I'm not sure if you would consider those an upgrade from your Lexicon. Theta is certainly another company to consider.

What speakers are you driving?

Theta is very good. Some people even use them to bi-amp their two channel systems.