Guy, this is probably the answer you are anticipating, but hoping you wouldn't see.
The Lexicon Omega is a somewhat dated device. It is USB 1, and the ASIO drivers are marginal. At best, it will deliver almost tolerable latency. Sorry to be so blunt, but it is what it is.
I like the concept of the Omega. It has a very cool layout, and basically good I/O control, but its physical limitations are its downfall.
Most contemporary interfaces will allow you to record while monitoring the effects through input echo at imperceptible latency. I don't have an actual amp here, so recording with amp sims is a matter of routine.
I use an Akai EIE Pro because it has some unique functions, but there are dozens of suitable interfaces that will do what you want. Sadly, the Omega isn't one of them.