The closest international airport to Lund is Copenhagen Airport (Kastrup) in Denmark. It takes about 35 minutes from the airport to Lund Central Station by train. Train tickets can be purchased from the Swedish Skånetrafiken ticket machines or the Danish DSB ticket machines or DSB ticket office in the arrivals hall at Copenhagen Airport. Please note that you need to buy the ticket before you enter the train. Groups of two or more people will get a discount buying the Duo/Family/Together ticket. If you buy a ticket Copenhagen Airport-Lund it will also be valid on the tram from Lund C to MAX IV.
The closest airport is Malmö Airport. From Malmö Airport, there are coaches (“Flygbussarna“) to Malmö C where you can take the train to Lund C.