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When you catch Solgaleo/Lunala and it gets sent to the PC, a message that says "try bringing them back here" or something along those lines. Seeing as taking Solgaleo to the Altar of Sunne did something of note, it follows that something of note may happen if you take it to the Lake of Sunne.
Necrozma was hinted at by Looker, so you know that it's somewhere on Melemele Island. You can always just use a repel, walk around in each area and see if it appears.
