You can only activate the ① effect if you already have a "Lightsworn" monster in your GY. However, when choosing a target, you can choose to target the card you discarded, instead.
If you control multiple "Lightsworn" monsters, their End Phase effects don’t chain to each other (they each activate, one after another).
Discarding 1 card is a cost to activate this effect.
If you discard a Level 4 or lower 'Lightsworn' monster to activate the effect of "Lumina, Lightsworn Summoner", you can Special Summon it.
You cannot activate the effect of "Lumina, Lightsworn Summoner" if you do not have any Level 4 or lower 'Lightsworn' monsters in your GY, even if you would discard one to activate the effect.
If an effect is chained that removes "Lumina, Lightsworn Summoner" from the field, the targeted 'Lightsworn' monster is still Special Summoned.
See "Jain, Lightsworn Paladin" for additional rulings.