You can fly to Lesvos island and land to Mytilini (MJT) airport either by taking a charter flight from specific locations around Europe or by taking a domestic flight from Athens or Thessaloniki airports.
Charters fly usually from UK, Denmark, Holland and Germany. Usually the companies fly on specific dates of the week, so people tend to stay for a minimum one week in the island. The benefit, apart from the more attractive price, is also the saving of time, since the stop to Athens is avoided.
Check the following websites for more information and direct bookings.
Domestic flights schedule can be checked in the following website