Best way to think about it is that it's essentially the same system as FFIX. Instead of wearing equipment until you fill the AP requirement, you just have to wear it for four fights. After that, anyone can use the ability if they have enough points to spend.
Once *any* character has used a Pictos in four battles, the Lumina becomes unlocked for the whole party and can be equipped by any character for its Lumina Points cost. It is not permanent, as it can be deactivated at any time to regain the used Lumina Points.
Even once the Lumina has been unlocked, a character can still equip the Pictos for the stat bonus, and to get the passive ability for "free" (no Lumina Points required).
Not permanent, just a cost to activate it. You can always inactivate and swap as you please to fit your current build. And once the Picto is “unlocked” after 4 battles , any character can use it via Lumina pts.
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While the Pictos is equipped on a character, that character gets the stat bonus and the Lumina/passive without having to use any Lumina Points.
It’s a way to get you to “test drive” the perks.