And that’s all it is – an example;
likewise, the LXDM Greeter style and theme – an example.
The relative size and positioning of the login controls can vary according to the Greeter you choose and the theme you choose.
You can also customise the theme (make your own theme) if you wish; however, you would need to research that yourself.
This is true no matter which Display Manager, or which Greeter you choose; there are often many ways to achieve the same result in Linux.
Subjective, at best.
I’ll simply say that you’re not right. Many DM/Greeter combinations share that honour of being lighter than SDDM or GDM, for example.
CDM, XDM, LightDM and LXDM are arguably lighter.
SLiM, Console TDM, and Ly are lighter still.
However, none of these are ideal for every distribution; some are abandoned or unmaintained for a very long time; some are incompatible; some are missing features that most have come to expect.
As has been said, LXDM is no longer used by any currently available Manjaro edition; neither Official or Community – but, LightDM is.
This also infers that LXDM is largely unsupported. It’s in the Official Repositories; no doubt it’s also available via the AUR (I haven’t checked), so it can still be installed, but how long it may be a viable concern is anyone’s guess.
The logic seems clear. Use a supported DM, find (or create) a theme and Greeter to satisfy your desire.
Incidentally, it’s quite possible to duplicate the look and feel of that LXDM Greeter in LightDM, with a little effort; possibly using the Slick Greeter as a starting point.
Another important consideration – is it compatible with Wayland? It’s only a question of time before most every Linux distribution will make the switch from X11 to Wayland.
Wayland is already the default on Gnome and Plasma; and KDE plan to remove X11 completely. Much to consider, indeed.
Unofficially, as was hinted at earlier, some members regularly maintain custom Manjaro distributions (spins).
@Jim.B (for example) maintains quite a few:
Perhaps one of these will already have a similar Greeter.
Otherwise, all we can really do is to wish you luck.
Regards.