Chromium in Launchpad but not in Applications
I know I just asked, but I figured it out and want to post the answer for others when they search for this same problem. Run the following in Terminal:

cd ~/Applications
rm -rf APP_NAME.app


Note: If the app name contains a space, place a \ character before the space so it looks like this /My\ Space

I verified that I was removing the correct app first by renaming it then checking LaunchPad to confirm the change. Once I saw that I was actually changing it in LaunchPad I went ahead and deleted it with the rm command.

You can additionally write rm -rf (with a space after the -rf) and then drag n’ drop the application from the Finder window into the terminal window. This will paste the path to the application correctly (auto fix spaces, etc.). Then press enter. This will ensure you have the correct path and are deleting the correct application. 

Warning: Do not press enter without a path after rm -rf