The single best thing to do in Lamu is to spend a day on a sailing dhow. The captains hang around the seafront and the deal is straightforward — you choose a destination (Manda Island, Kiwayu, the Takwa ruins, a snorkelling spot), they sail you there with a packed lunch of grilled fish and pilau on board, and you pay at the end.
A typical day trip leaves at nine, sails for an hour or so, drops anchor at a beach for swimming, has a charcoal-grilled lunch on deck, then sails home through the afternoon. Bring sunscreen, a hat, and small notes; tip the cook separately at the end of the day.