Lodz Wladyslaw Reymont Airport (LCJ) currently has connections via Munich and Amsterdam and low cost Ryanair connections.
An alternative is to fly to Warsaw Chopin Airport and take a train from Warsaw to Łódź Kaliska. In order to get to Warszawa Centralna (Central Railway Station) or Warszawa Zachodnia from Chopin Airport, use the train (line S2 or S3) operated by Szybka Kolej Miejska – SKM (Fast Urban Railway).
http://lotnisko.lodz.pl/en (Lodz Wladyslaw Reymont Airport)
http://www.lotnisko-chopina.pl/en/passenger/access-and-car-parks/train (Fast Urban Railway)
http://www.ryanair.com/en/flights-to-lodz/ (air connections)
http://en.e-podroznik.pl/ (rail and bus connections search)