You must defeat the elite 4, then go to mistys city, then north. Talk to Bills grandpa, and he want to see Pokemon. I think it is theese Pokemon he wants to see. Lickitung, Staryu, eevee, Pichu>>Set pikachu at the day-care with a ditto, in the egg it's a Pichu<< he want's to see a vulpix too. That is for silver, in gold can't you catch a Vulpix, so i think it's a growlithe instead.
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Yes, use a water stone.
In order of how he wants to see them (based on Heart Gold and Soul Silver): Gold/Heart Gold: Oddish - Leaf Stone Growlithe - Fire Stone Pichu - Thunderstone Jigglypuff - Everstone Marill - Water Stone Silver/Soul Silver: Lickitung - Everstone Oddish - Leaf Stone Staryu - Water Stone Vulpix - Fire Stone Pichu - Thunderstone
use a water stone o evole it
You need to get to Bills Grandpa in Cerulean (Kanto), he will ask for a pokemon. The first is Lickitung, the second is Oddish and the last is staryue, i think that you then get the water stone from him. I hope this help :)
you can use a water stone on lombre