Dude is asking for a Pokemon that looks like the sun and starts with Sol. So Solrock. In Pokemon Moon he asks for a similar Pokemon who is Lunatone. But you can't get them in this game. So I'm wondering what happens when you have one in your party while talking to him.
If you show the old man Solrock or Lunatone, he remembers his home and gives you a Moon Stone. He also talks about other more deep stuff, but you can research that.