This is fixed by the following hack:
`su -` or maybe even `su`, opening another display.

Only `su -`.

This issue is covered here:

https://wiki.parabola.nu/OpenRC#Launch_X11_without_root_access

Also it was already covered #2271
Please do check for existing BRs before filing a new one.

i think this is about the behavior of the LiveISO, not the installed system?

In that case then this changes to a "info needed". Just tried the iso (parabola-openrc-lxde-2019.03.11-dual.iso) all apps I clicked worked,
Opened a terminal. apps launched from the terminal work (Terminal defaults to user root)

Can the OP please provide steps to reproduce.
Thanks

I have opened lxterminal, done something (not sure what), then all applications refused to start, including new terminals (not windows).
This issue cannot be reproduced in other ttys.

I'm not sure as I have not installed it.