Sweden uses the Swedish krona, not the Euro. Nearly all places accept card payment, but some do not accept cash. In Sweden it is not necessary to have cash. Denmark uses the Danish krona.
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. Simplest is to install the Skånetrafiken app on your phone and use that for the train and bus expenses.
Note: There is passport control when travelling between Sweden and Denmark on the train or by car using the Öresund bridge. Make sure to always bring a valid passport when travelling between Denmark and Sweden.
Lund also has an excellent bus network. Buses do not take cash payments and the Skånetrafiken app is the simplest option. Alternatively, payments can be made by swiping your contactless credit/debit card.
For more travel information, please visit the ESS website.