How do I set a per world group (multiverse) so that a player could have group 'Example' in the world 'Example_World' but have the group 'Test' in the world 'Test_World'?

Do /lp user USERNAME parent add example world=example_world
/lp user USERNAME parent add test world=test_world

See here:

• https://github.com/lucko/LuckPerms/wiki/Command-Usage#what-is-context
• https://github.com/lucko/LuckPerms/wiki/Command-Usage#lp-usergroup-usergroup-permission-set