Turtwig is a Hoenn region starter Pokemon. Thus, it cannot be found in the wild for capture in HeartGold. However, after defeating Red at Mt. Silver, you have a chance to get a Turtwig. Go to Silph Co., talk to Steven (the Hoenn champion), and choose the green stone to get a Turtwig.
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link trade from diamond pearl or platinum
at the begining of the game the profeser will give you three Pokemon and you have to pick one and those three Pokemon are turtwig chimchar and piplup and if you want turtwig pick turtwig.
It is not possible to catch a wild Turtwig on Pokemon Diamond. It is generally impossible to find and catch Starter Pokemon in the wild. This was a mechanic designed to encourage player interaction for trading.
Turtwig does not appear in Pokemon Sapphire, or in Hoenn for that matter. Instead, you can find Turtwig in Generation IV (Diamond, Pearl, or Platinum).
You can catch Lombre in Pokemon HeartGold in the Safari Zone at a waterside area once you receive the National Pokedex.