There is no Lilycove in Pokemon Diamond or Pearl. Lilycove is exclusive to GBA Pokemon Games Ruby, Emerald, and Sapphire.
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Pokemon Ruby= Magma Hideout at Lilycove Shore Pokemon Sapphire/Emerald= Aqua Hideout at Lilycove Shove Pokemon Diamond/Pearl= After you beat Cyrus at Veilstone City
North of Lilycove....
most of the time you can get them from the department store in your game. in Pokemon ruby the department store is in Lilycove city. In Pokemon diamond and pearl it is in Veilstone city.
In lilycove specifically there's nothing to do besides the Pokemon contests.
The Lilycove Department Store is in Lilycove City, up the stairs behind the POKeMON Center.
Its in Lilycove or Slateport. Its in Lilycove or Slateport.
Yes in Lilycove City
If your Pokemon scores five hearts or more in a contest, you'll get a portrait of it that will go to the Lilycove Museum.
Surf to an island
In Lilycove town
Next to lilycove
From lilycove city if you go east you can reach mossdeep city.