The accepted answer resolves the issue of Lubuntu's dubious use of the BROWSER environment variable, but that's just one finger in a dike with a whole lot of holes. Setting a default browser in Linux is like playing Whack-a-Mole, you fix something that works in one app, some other application has another way that's still broken.
It's almost understandable that Lubuntu did it that way, the environment variable pre-empts most (but not all) ways of launching a browser, so that was actually something they could reasonably control; problem was, it was different than the "standard" way to do it, they didn't (as far as I can tell) document a way to change it, and frankly environment variables ought to belong to the user.
So. XDG utilities are FUBAR IMO, and, once you've followed the advice in the approved answer, you are likely to still have some cases were some program or app opens the wrong browser, thanks to XDG simply not working. For example, after I deleted the BROWSER entries in the lxqt config files, I was able to run
xdg-settings set default-web-browser without getting an error; except that it did not actually set the default web browser. Subsequent calls to
xdg-settings set default-web-browser continued to return Firefox as the default browser. Though I was able to get x-www-browser and sensible-browser to run my preferred browser, other methods still ran Firefox. Python's webbrowser module continued to open Firefox, for instance.
In the end, I decided scorched earth was the only way. I searched for every instance of "firefox.desktop" in various locations for config files, and replaced it.
find /usr/share /etc ~/.config -not -type d | xargs -d '\n' grep -F firefox.desktop
Once I changed them all, it would finally reliably launch the correct browser. But this won't likely work forever: an upgrade could overwrite some of those files.
And to think I switched to Linux long ago so I wouldn't have to deal with this Windows bull.