Because I could just as easily use a competing product that does work with Chrome. An all-or-nothing mentality with (free consumer) software isn't a great way to acquire new users. Switching my primary browser to use a password manager that I like is a ridiculous decision.

They make a mobile browser too so why make this app?

For iOS at least, you need an app to have first class password filling privileges. My understanding is android is becoming more restrictive about this and is locking down APIs such that you do or will need a native app for password filling on that too.

Turning the question around, Firefox also makes mobile browsers, so why should they have created Lockbox at all?

There are many reasons to want to use different browsers:

* Your spouse prefers a different browser

* Firefox doesn't work as well on MacOS as Windows/Linux

* You need to use multiple browsers for testing

* You currently use Firefox everywhere, but don't want to be locked into that decision.

The only reason I don't use Firefox Sync is because I don't want my password manager tied to single browser. I would have pounced on this in a heartbeat if a chrome plugin to Sync was available a year ago.

because many people use multiple browsers for variety of use cases.

same reason google provides their products for iOS environment, same reason there's a desktop outlook client for macOS, etc