Of the four carriers named by guv1976 TK only flies 2 or days a week between IST and LUN. And the flight arrives at 01:35. While I love flying TK, I would not recommend flying them to LUN.

All three of the remaining airlines fly from ORD to LUN on a daily basis.

ET departs in the morning and has an 85 minute connection at ADD for a flight to LUN that arrives in the early afternoon the next day. The flight from ADD to LUN alternates between a nonstop and a one stop direct (stopping in HRE).

QR departs in the early evening and arrives around 08:35 two days later with a 9 hour connection at DOH.

EK departs later in the evening and arrives around 14:30 two days later with a 14 hour layover in DXB.

If you fly in economy, I would recommend ET. Their economy seats a fairly comfortable and have a decent seat pitch. And the short layover is actually a blessing on this long a trip. If you are flying in business, both QR and EK have far superior business class products. But this typically comes at a significant cost.