The fastest way is by air. Air Calédonie flies from Nouméa's Magenta domestic airport to Wanaham aerodrome in Lifou's north — the flight takes about 40 minutes and runs several times a week. Book ahead; the planes are small and fill up.
The slower alternative is the Betico ferry from Nouméa, which runs twice a week (typically Monday and Friday) and takes around 5 hours 45 minutes. It's a comfortable crossing on calm days and costs significantly less than a flight. The ferry docks at Wé.
Cruise ships also call at Lifou — usually at anchor in the bay, with tenders to shore — but this gives you only a few hours on the island.