The Lighthouse is a required dungeon because it contains the Star Crest which is required to complete the game. In order to receive it, the heroes must defeat 4 Gremlins which are disguised as an old man.
Floor 1F - ~500G
Floor 2F - Star Seal
Floor 4F - ~725G
To find your way to the Star Seal, you must first take the southwest staircase from the first floor. On the third floor, take the first staircase you find. On the fourth floor, go right, up, and then left along the edge of the tower. Make your way up to the seventh floor, and follow the gremlin into the building. Take the stairs on the very bottom leftmost tile and follow the old man to your prize.
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5 Sigils • Celestial skein • Echoing Flute • Eye of Rubiss • False idol • Golden key • Jailor's key • Moonshard • Ra's mirror • Ship • Silver key • Subtle shuttle • Sunken treasure • Teleportal • Floodgate key • Windbreaker • Yggdrasil leaf