Your Three Real Options
The fastest way to Lampedusa is a direct flight from Palermo or Catania, both served by Aeroporto di Lampedusa (LMP) on routes operated by several carriers, which vary by season. The crossing is roughly an hour in the air — long enough to clock the colour change in the sea below, from Sicilian blue to something distinctly African. Palermo tends to have more frequency in high summer; Catania is worth checking if you're arriving into Sicily from the east. Fares spike hard in July and August, so booking early isn't a tip so much as a rule.
The second option is the overnight ferry from Porto Empedocle, the small harbour town just south of Agrigento on Sicily's southern coast. Siremar operates this route; the sailing takes around eight hours, arriving in the morning. You board in the evening, sleep (or mostly sleep) in a cabin, and wake up with Lampedusa's low profile already on the horizon. There's something to be said for arriving by sea — the port reveals itself slowly, fishing boats already out, the light already warm. You also skip a night's accommodation cost, which on a small island isn't nothing.
The third option, technically, is the ferry from Linosa — but that's only relevant if you're island-hopping the Pelagie already, not arriving from scratch.
Which to Pick
Pick the flight if time is short, if you're travelling light, or if you've booked high-season accommodation that has a strict check-in window. The Palermo–Lampedusa route, in particular, can feel busy in peak weeks, so choose your seat and check baggage limits carefully — the aircraft on these short hops are often small turboprops, not jets.
Pick the ferry if you're in no hurry, if you enjoy the ritual of departure — a drink on deck, the mainland lights fading — and if you want to arrive feeling like you've actually travelled somewhere, not merely been relocated. The overnight crossing suits people who sleep on boats. If you don't, a cabin is still better than a seat, and the morning landfall is genuinely worth it.
One thing both options share: Lampedusa is at the end of a logistical chain, and that's part of the point. The slight effort required to reach it is exactly what keeps it from feeling like everywhere else.