Babi Lighthouse is to be an enormous structure, built by Babi of Tolbi, to help his navy find the lost city of Lemuria. Construction hasn't been going on long, so there's not a lot to it yet. Rumor has it that they used some existing ruins as the structural foundation...
Upon entering the Lighthouse area, you will see many men standing around. Due to the events currently unfolding, they are unable to work for today. Head to the right as far as you can. When you see one of the Carry Pillars, push it two spaces left, then use Move to slide it one north. Now, stand in front of it and use Carry, dropping it on a slightly elevated area to the left. Climb down, then go up two ladders on the left and jump across to collect the Lucky Pepper from the chest.
Once you've got it, head north to the next map. There's a bunch of soldiers and workers lying on the ground, and a ladder heading underground to the left. Climb down there, and once inside, jump across to the platforms. Move the pillar one space left, then go back up. On the side opposite of the ladder, there is a pillar in the center of a bounded box. Push it out of the way, then climb down the ladder underneath. Use Move to slide the pillar to the left, out of your way, then jump across. Go up the ladder, and outside use Growth on the small plant. Climb up the vine, then walk over to the slide and slip down. Enter the door, and inside slide down into the hole at the center of the room. You will land next to a Jupiter Djinni; engage it and add Luff to your group. Congratulations on gathering all the Jupiter Djinn. Once it is defeated, slide down again.
Go left up two sets of stairs, and then slide down the northern edge. After falling through two floors, you'll land in a cave-like area. As soon as you walk around the corner, a cutscene will begin. Faran, Sheba's guardian, is here with a small group of people. After they finish, walk over to the door and use Reveal to expose a button. Press it, and the doors will open, starting a new scene. When Iodem tries to walk through the door, it shuts. Only adepts may pass from this point, so you're now on your own. Iodem and the others will wait there. Open the door again with Reveal, then pass through. Go down the stairs, and you will be back in the Statue room of Venus Lighthouse.