orangesporanges
Set the guitar track input to "none"after recording.See if it goes away and report back.

Setting input to none made no difference. 
 

ChristopherM
Go to Control Panel - Power Options and ensure that you are using a High Performance option.

 
Already set to High Performance, and for a few days at least I don't even have screen savers enabled. Minimum Power State was already at 100% (good thought though).
 
Some experimenting with the various amplifies shows quite a bit of cross-channel distortion. So at least we are narrowing it down. But it is still weird that effects on the lead guitar track make the clean acoustic guitar track sound dirty/clipped/distorted.
 
 

ASIO: Using the ASIO driver that Lexington provides for the Omega interface.
 
This. Sorry, but there has never been anything good said about these drivers. 
A new interface with trusted drivers is you best bet. 

Additional diagnostics:
I cut to MP3 exports, one with the amp simulator and one with the distortion pedal (see notes above). The same degree of cross-channel distortion was present in the MP3 files.
 
Perhaps there is something I don't understand about Sonar, but I would think that rendering the MP3 files would not have real-time, latency dependent issues. Since the induced cross channel distortion occurs in real-time (output over the Lexicon) and in the MP3 file, I think something else is afoot.

Two thoughts:
 
Rendering may be happening in real time or not depending upon how you have your settings. Also, I think some plug-ins only support real-time processing.
 
What happens if you mute the track with the intended distortion during playback? The mute does not prevent the CPU-load from the processing of the signal. It only prevents the processed signal from getting through to the final mix. If the unintended distortion does not go away, that would suggest it is something to do with CPU contention or overload of some kind. If it does go away, that would suggest some kind of intermodulation effect, which would make me look very carefully for unintended signal routing between tracks and buses.

I think the real problem is that Lexicon drivers are not good and the O/P is looking for something complicated. I suggested he try WDM drivers instead of ASIO but he didn't say if that helped.

^^ To which I would add also try the MME drivers, which is your basic lowest common denominator audio drivers. When troubleshooting always try the simple stuff first.

Well, now we have a real stumper.
 
Finally had a chance to return to the studio and the problem went away. I configured the amp simulator  to what in the past was the most hoggish, nosiest configuration and it was the only distorted channel. I double checked the board to make sure nothing else had been tweaks (no telling what random keystroks the cats type when I'm out of the room) but it all looks the same.
 
We must remember, this is a Window-based DAW, so random stuff is expected.

Balls.

And just as mysteriously as it went away, it came back (Sweet Jesus, this is balls).
 
So, a bit more experimentation tonight before heading out for an open mic. I watched the CPU load a bit more closely. With the amp stack on, the CPU peaked at around 70%. But I noticed the CPU load was less erratic when the amp (not anything else in the simulator) was bypassed.
 
For giggles I deleted the stack I was using and tried two others, including the odd little amp sim that comes with Sonar. They all produced the cross channel distortion, and all quit it with a simple bypass.
 
I cranked the ASIO latency control to the highest level (most buffer). Only a extremely slight improvement (basely noticeable).

What's your processor and amount of memory?
Have you followed the Friday's tip of the week that related to removing extraneous drivers that degrade performance?
 
Guitar amp sim distortion traditionally draws a lot of CPU. At this point I'm beginning to think either your computer is underpowered, or something is compromising its power.