yes after you defeat the elite four again note: they'll be level 70 and higher harder then red times 5 you wont probably get through to the 3rd one but... I did.
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You can catch Lombre in Pokemon HeartGold in the Safari Zone at a waterside area once you receive the National Pokedex.
After a while once you battle a lot with the Pokemon (without letting it faint to much) then it will start to like you more. That's what I did with my dratini and it really likes me now :)
Once beating whitney, you get the watering can, water it XD
You Find it in the Vermillion City Pokemon Club. and Then once you have it just go up to her and press A
you dont get the pokeflute you use the pokegears radio once you can in kanto and tune it to the pokeflute channel