The full-service agency, which was launched last year by Abbott Mead Vickers BBDO and PHD's Rocket, picked up the business following a four-way shoot-out.
Axis Communications, the incumbent on the business, was involved in the final pitch.
Lunar will be briefed to develop a campaign to give the Abercrombie & Kent brand standout against competitors in the luxury travel market, including Kuoni, Carrier and Cox & Kings. It will also reposition the business to attract a broader client base.
Abercrombie & Kent specialises in creating bespoke holidays for high earners.
Lunar works across PHD and AMV clients. In January this year it picked up its first piece of new business when it won the Gallo Wines ad brief.