The best and cheapest way to get to Lund is to fly to Copenhagen airport (Kastrup) in Denmark, and then catch a train to Sweden and Lund. Another possibility is to fly to Sturup airport in Malmö, and then catch a bus or cab to Lund.
Trains from Copenhagen airport (Kastrup) to Sweden and Malmö/Lund leaves about every 20 minutes. Follow the train signs downstairs to the platform. All trains to Sweden go to Malmö - and more than 50% of them will then continue to Lund. Otherwise, ask the train attendent where to catch the next train from Malmö to Lund.
The travel time to Lund from Copenhagen airport (Kastrup) is about 45 minutes if you don't have to change in Malmö and about 7 minutes longer if you do need to change.
NOTE: It is a good idea to buy the train ticket before getting on the train, becuase it is much more expensive to buy the ticket on the train. The tickets can be bought at Copenhagen airport (Kastrup) before you go downstairs to the train platform.
Detailed information about train departures
(Enter Kastrup as departure and Lund as arrival in the journey planner)
Buses from Sturup airport leaves every hour and the travel time is about 30-40 minutes. A cab will take you to Lund in about 15-20 minutes.