USB as an active input

Can the USB on a micro-controller like the Lillypad be programmed to actively take in information and process it like any other input?

The micro-controller board typically has 2 chips on it. One interfaces with the USB socket, and converts the USB data to serial data and serial data to USB data. The other reads and writes serial data, and collects input from and sends output to digital pins, and collects input from analog pins.

That chip does not have direct access to the USB data, and the USB chip is typically powered by the USB cable.

That chip acts as a USB slave, not a USB master. So, the usual answer to your question is no, the micro-controller can not directly interact with the USB port. That would require that the micro-controller act as a USB master, which it is not designed to do. There are USB master shields available, with a separate USB port, but NO software. You get to right that software.

Having said all that, it isn't clear what you envision connecting to the USB port on the lilypad/Arduino, so there may be possible solutions.