Our company is currently reviewing all of the options for upgrading to an LMS. We first need to find an LCMS. Any recommendations?

I'm not sure what you're asking.
An LCMS is generally an LMS + other features, largely the capability to author content within the LCMS environment.

So when you say 'upgrading to an LMS'...what are you upgrading from? Nothing? A simple internal website?

Are you looking more for the differences between an LMS and an LCMS so you know which direction to go?
Here's a generic write-up:
http://www.kendallhunt.com/index.cfm?PID=2481

As to recommendations, can do, but maybe narrow-down what you're looking for a bit more.
CM