You can catch it in the Bell Tower, Burned Tower, and Sprout Tower on Wednesdays when the radio is playing Hoenn Sound, and also in the Safari Zone (Plains area with 15 forest objects or Savannah area with 10 plains objects). The Safari Zone version is much higher level.
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You trade for it.
yes you can.
You can catch Lombre in Pokemon HeartGold in the Safari Zone at a waterside area once you receive the National Pokedex.
Find and then catch
You can't catch it. It's a starter pokemon.