It seems to make more sense to use 19.04/LXQt since, if you’re using Qt, it already is running it.
qtserialbus, from what I can tell, has never existed in the Ubuntu repos since before Disco/19.04 with an upload of 5.10.1 to the development version at the end of 2018. The first upstream release according to their GitHub was 5.6.0 at the beginning of 2016. You can blame Debian for this, though. An ITP (intent to package) was filed in 2017 but wasn’t finished until the next year, at which point it pretty much went right into Ubuntu.
Still, in Qt terms, that’s a relatively new piece of software. You’re not going to find a Qt4 version of it, for example.
If you’re doing Qt development, it might be better to ask at their forums.