I can't use /lp user [user] parent add [group] (command-no-permission message) with * and luckperms.* permissions, all other commands like permission set or editor or applyedits are ok. Tested with argument-based-permissions enabled/disabled.

Server: paperspigot-1.12.2 (b-1648), LuckPerms 5.0.83

Can you show the actual response of the command?
And you can always use Verbose to debug stuff and see what may be checked.

Response is command-no-permission message.

I can use any other command, but not this.

Response is command-no-permission message.

This isn't a valid response at all as LP never returns this. So either another plugin is sending this (And blocks LP for whatever reason) or you messed something up.

Provide actual information, like screenshots and such.

I mean this message from lang.yml

I can use any other LuckPerms command, but not parent command.

Check with verbose - Andre linked the wiki page for it to you above.