The lost and found solution at Ataturk is very weird and I still don't fully understand how to properly use it, but I did manage to get something back once so let me tell you how it went. I was flying Int-Int with my wife and on the way to Ist she left her tablet on the plane. She realized that when we were in the lounge. We talked to the lounge desk, they made some calls and told us that the tablet is in the lost and found in the domestic terminal and we need to pick it up ourselves. So we went to the land side and then to the domestic terminal. In the domestic terminal we learned that the lost and found is on the air side near baggage claim, but we had no way of getting there since we didn't have domestic tickets and there is no procedure to let the international passengers get to the lost and found. Eventually we went to the exit gate from the baggage claim and after long convincing of a security guard that almost didn't speak any English he let my wife thru and I stayed with him as a collateral. Eventually she got her tablet back but there must be a better way to do it than what we did. Thankfully I booked long layover to enjoy the lounge so we had enough time for this adventure.

I don't believe they are selling your lost possessions for profit, in fact if you don't pick it up it creates a cost for them because they have to store it. It's just a typical example of poor organization on TK's behalf.