There are two options. Either Milano Malpensa airport in Italy, or Zurich Airport. Malpensa is closer geographically but with the train connections it will be about the same travel time from either airport to Lugano (about 2 hours). It may be easier to fly into Zürich since there are quasi-direct trains from flughafen Zürich to Lugano every 30 minutes to an hour and the train takes only slightly longer than 2 hours. Flights into Malpensa may be more economical since the airport is well served by budget carriers.
There are quite some options for traveling to the nearest airport. The nearest airport to Erlangen is Nuremberg (NUE) Airport which is 11.9 km away. Other nearby airports include Munich (MUC) (148.8 km), Stuttgart (STR) (165.7 km), Frankfurt (FRA) (182.1 km) and Memmingen (FMM) (186.9 km) which are easily connected with public transports.