From my understanding, Lockwise is either a redesigned stock Firefox password manager, or the one written from scratch as addon for Firefox PC (which was lately implemented as part of the web-browser in v70) and available as a mobile app to provide one with all the passwords they've used to login on websites (note that all the passwords you stored before Lockwise became a thing are still saved), as long as they're synced with your Firefox account, thus they're all saved on a server and are being downloaded on each machine you log into your account on.

As for exporting data, I'm afraid there doesn't seem to be such an option (at least so far). You could, however, check out this question if the solution is still relevant for Lockwise today https://support.mozilla.org/en-US/questions/1258644

As of Firefox 70 Lockwise is the new logins manager inside Firefox. It was tested as an optional add-on named "Lockbox" prior to Fx 70.

Your login credentials are stored inside your local Firefox installation. If you use the optional Sync feature your login credentials will be synchronized with your other Firefox user data, but the data types can be selected / deselected thru about:preferences#sync .

As far as "other password managers" go, compatibility is up to those other "managers". Mozilla has not created an "export feature" for logins data, but the 2 files can be copied from the Profile folder. Overall, if an external password manager is made to be compatible with Lockwise inside of Firefox - it should work.