I ordered the lamp from a company called Advanced Lamps.
In order to make sure I received the right replacement, I moved the TV and found the actual part number for my unit KF-42WE610.
When the lamp showed up, I had a hard time finding clear instructions for the swap. For this reason, I took lots of pictures to help everyone else out that may have a similar model TV.
Step 1: Around Back
Wait at least 30 minutes if the lamp was just on.
Find a thumb screw and loosen it all the way. Next find its match on the other side of the TV and do the same. It is a fine thread so there will be lots of twists.