There are a few steps when it comes to this, and indeed I even overheard airport staff in Calgary yesterday discussing this.
- If it's lost on the plane, then you speak to the airline. That's the only time it's worth contacting them.
- If it's lost in the airport, you need to deal with the airport.
Now, with regards to them not answering the phone, some steps you could try:
- Try the phone again making sure to call during Dubai business hours
- see if there's an email address on the airport website
- try filling out the lost and found form again - perhaps it didn't get through the first time
- my favourite method lately - try their twitter account: Dubai Airports - it's amazing how fast airlines and other companies have responded to me when my complaint/query is out there in public on twitter.
- If it was in Terminal 3 - this is one of the rare times that the airline handles it as well - because Terminal 3 is Emirates-only flights - you could call Emirates on +971 4 0505 7584 / 7538.
- Try their Facebook page - it's amazing how much faster companies' social media sites reply sometimes.