The Suite Key is actually found inside the abandoned house on Route 213. It is located in the corner of the upper floor, behind a bookshelf.
Once you obtain the Suite Key, you can use it to open the locked door on the second floor of the house and access a secret area that houses the Lake Acuity Pokémon.
Please note that there is no mention of a lady losing a Suite Key at Valor Lakefront in the game.