Not only Firefox, but also other non-elementary Apps.
AFAIK the AppCenter only shows apps whitin the Ubuntu Store and sources. If those apps you have aren't on the official repos they won't show up there.
- In the repositories included with Loki.
- Have an AppData file that conforms to specification OR
- Have a .desktop file that conforms to specification.
That said, Firefox appears in my AppCentre.
sudo apt update
This may be related to an unfixed bug:
Expectation: AppCenter fires up packagekitd and updates the software catalog transparently in the background when the session starts up
Reality: AppCenter only shows data for the pre-installed packages. packagekitd never fixes it. AppCenter is useless until you open a Terminal and manually run apt update