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.