The Lighthouse is Shantae's home on the coast near Scuttle Town. It is housing provided by the Mayor of Scuttle Town as part of her job as the town's Guardian Genie, and allows her to watch the seas for enemies (in particular, pirates like Risky Boots).
The Lighthouse is the starting point in every Shantae game in the series so far.
According to Matt Bozon's interview for the Shantae wiki, the Lighthouse is the last remnant of an Old Scuttle Town that used to sit in the small cove where it is located. From there, Shantae can have a long view of the town.
In the canceled  The lack of such feature in may mean it was dropped altogether., it was shown to have a backdoor hatch leading into the sea. It could have been accessed by hair-whipping the stairs leading to the Lighthouse's door.
In, we briefly see the inside through cutscenes. Shantae notes that she doesn't own a bathtub.
WayForward stated on the Kickstarter page that they have had sketches of the interior of Shantae's Lighthouse since the era, but Half-Genie Hero will allow the player to explore it for the first time.