Does Autofill work with all browsers?

The title is pretty much my question. I don't like Chrome because it sends me really inappropriate ads. So I use Firefox for most browsing, and the Keyboard Browser occasionally.

The Password Keeper doesn't automatically fill the login information with anything other than Chrome, so I just copy and paste when I need to. But I was hoping that Autofill would fill (sorry!) that gap in functionality. Does it?

I use LastPass and it doesn't look like autofill is supported. I would be happy to find that it actually is but so far no login seem to have been autofilled for me using LastPass.

My understanding is this is a limitation of mobile Firefox as they don't provide access to the required api/etc due to their privacy protections.