Are the two libraries essentially identical?
If not, what particular actions demonstrate the clear discrepancy or incompatibility between the two APIs?
Basically, I might really be asking,
Qt is used on many systems; you may learn more from https://contribute.qt-project.org
Youâll find it used by Microsoft Windows apps, on Apple MAC OS, and its foundational to the Android desktop on many of our phone/tablets.
Long ago it was made free for much open source work (when on computers; ie. Linux/BSD), but the the FSF still didnât like that it was owned by a corporation, thus the creation of GTK as an alternative (creating that from the Gimp Toolkit), so there is a lot of history.
Qt is managed on Ubuntu by Ubuntu-Qt, so those using it (which include Lubuntu & Kubuntu, as well as Ubuntu Studio which use the KDE Plasma desktop as well) all have a say on what version is found/default in the libraries, so on each release all will be using the same Qt version by default (some upgrades maybe provided by PPA; but thatâs not the default).
Code is also brought from upstream Debian-Qt-kde too, with LXQt using the same code there too.
The Qt used by Lubuntu & Kubuntu is the same.
Those Qt libraries donât do everything that KDE Plasma requires, thus KDE Plasma also uses KDE Frameworks, and its here that KDE Plasma & LXQt differ; in that LXQt doesnât also use KF.
KDE [Plasma] is a desktop (or project), and I donât see it as an OS.
Kubuntu uses the KDE Plasma desktop which is Qt based yes, but it also needs KDE Frameworks which I suppose could be seen as extensions beyond what Qt can provide.
Lubuntu uses LXQt which aims to be light thus doesnât go beyond Qt (using KDE Frameworks (KF) for example). Though Lubuntu does use some KDE apps (KDE Partition Manager as example) thus some KF is included on a Lubuntu install, but KF is only used when youâre using those app (ie. KDE Partition Manager is running).
Ubuntu 24.04 LTS (ie. Kubuntu 24.04 LTS & Lubuntu 24.04 LTS) remained on Qt5, as the flavors (in Ubuntu-Qt) decided to stick with that version, rather than all switching to Qt6. Qt6 became default at 24.10.
I donât see any differences between Qt in both KDE Plasma and LXQt, or Kubuntu and Lubuntu.
Thank you VERY much, Chris, for that clearly explained overview of the Qt eco-system! I feel like I actually understand the ramifications for each to judge approapriately âhow to jumpâ ⊠IF ⊠I were inclined to do so. 
From my outsider perspective, I was thinking there was some unnecessary overlap. But, from your explanation, I understand now that Lubuntu is for the Qt âpuristâ, whereas Kubuntu (attempting to keep in sync with KDE) is delving into that framework to implement a cross-over between GUI and OS, which also explains the KDE Development Teamâs strategy in pursuing that, now that they have announced their own Linux distro codenamed âBanana Projectâ!
⊠And while I understand their desire to extend the reach of GUI integration with the underlying OS, I am not convinced that it is wise to make an OS that has only one âfaceâ presented to the Consumer, because everyoneâs mind works differently, which is why every one of us has our own way of approaching the challenges before us and the methods and tools that fit those unique approaches to reaching our goals.
As always, only time subjected to the crucible of life will tell whether their approach was the right one.
For me, the golden rule, which they seem to be breaking, is
which is my underlying issue with Canonicalâs push to impose SNAP-based packages on their Users (but that is a different discussion and would rather not go down that garden path here ).
Not sure about that interpretation.
LXQt aims to be Light, what that first L stands for.
As Qt itself isnât based on a single system, but is a rather broad toolkit (why Android uses it on phones! why itâs useful for apps running on Microsoft WIndows!), it doesnât provide everything an OS needs; thus KDE have created a framework that fills in for what is missing; ie. KDE Frameworks.
As I see it; if LXQt took advantage of KDE Frameworks (KF), theyâd become closer to KDE Plasma for starters, but more importantly theyâd also be ignoring the light aim.
Lubuntu just uses LXQt (& their apps, filling in for gaps as LXQt has fewer apps); Kubuntu just uses KDE Plasma (& their apps).
Theyâre both using the same Qt, so to me a âpuristâ can use either; the Qt stack is identical between them.
I know little about Banana Linux; the page you provided mentions an âimmutable baseâ which is a decision that has effects on what it is & isnât; but it does allow them to concentrate on other things (like their packaged KDE Apps and not the OS itself) would be my view. But this view is one quickly drawn here from reactions to what I read, and my view may differ if I learn more. I can see reasons for such an OS, but thatâs not for me right now.