How do you get lyra to let me use surf at new bark town?

To get Lyra to let you use Surf in New Bark Town in Pokémon HeartGold and SoulSilver, you first need to obtain the Surf HM from the move tutor in the Pokémon Center in Goldenrod City. Once you have the HM, teach it to a compatible Pokémon. Afterward, return to New Bark Town, and during your visit, Lyra will approach you and offer to demonstrate how to use Surf on the water with your Pokémon. Make sure you’ve completed the necessary prerequisites in the game to trigger this event.