Lance the dragon trainer? He is in very many places in the game, but he is officially the champion of the elite four, so that is where I would tell you to find him.
If you mean that Team Rocket guy in Kanto, he's hiding in Misty's gym and then on the bridge north of Cerulean City.
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You must be at the Lake of Rage and use Surf to swim towards the Red Gyarados. Either capture or defeat the Gyarados and then make your way back to the bank of the lake, you will now meet up with the black cape guy.
You CAN'T find an Emolga on Pokémon Heartgold. It was introduced in Pokémon Black and White, which was released a whole year after HG/SS. Answer: You can't find Emolga on HG/SS.
You can find it in Pokemon Platinum, Pokemon Crystal, Pokemon HeartGold, and Pokemon SoulSilver.
Houndour, Houndoom, Lillipup, Herdier, Stoutland. Legends: Entei, Suicune, and Raikou. Find them in Pokemon Platinum, Black, Heartgold, and Silversoul.
Find and then catch