Very close. Antalya Airport (AYT) sits just inland from the eastern edge of the city, and Lara lies on the coast directly south of it. A private transfer to Lara covers about ≈14 km and takes around ≈20 minutes. Kundu, the hotel zone that continues east along the same shore, is ≈16 km and ≈26 minutes away. In summer traffic you may need a few extra minutes, but this is still the quickest transfer you can book from AYT.
For comparison, Kaleiçi, the old town, is ≈16 km and ≈25 minutes from the airport, Konyaaltı on the western side of the city ≈27 km and ≈35 minutes, and Belek ≈33 km and ≈40 minutes. Live prices for each trip are on the route pages: Antalya Airport to Lara and Antalya Airport to Kundu.