Official text published by the Embassy of Cyprus in Washington DC (http://www.cyprusembassy.net/home/index.php?module=page&cid=168):
Travelers arriving in the Republic of Cyprus may enter the Republic only through the legal ports of entry: Larnaka and Pafos International Airports, or the ports of Larnaka, Lemesos (Limassol), and Pafos.
All airports in the part of the Republic illegally occupied by the Turkish invasion forces, have been declared by the Government of Cyprus as prohibited ports of entry and exit, and no visitor should enter or leave the Republic through these ports.
As a result of the Turkish invasion and military occupation of the northern part of Cyprus, the port of Ammochostos and the Keryneia harbor are closed to shipping and navigation, and have been declared by the Government of Cyprus as prohibited ports of entry and exit, and no visitor is allowed to enter or leave the Republic through these ports.
Visitors arriving in Cyprus by air, may enter the Republic only through the International Airports of Larnaka and Pafos.
Version published by the US Department of State (http://travel.state.gov/travel/cis_pa_tw/cis/cis_1098.html#entry_requirements):
Since 1974, the Republic of Cyprus has designated Larnaca and Paphos international airports, and the seaports of Limassol, Larnaca, and Paphos, as the only legal points of entry into and exit from Cyprus; these ports are all in the government-controlled southern part of the island. Entry or exit via any other air or seaport is considered an illegal act by the Republic of Cyprus. Formerly, visitors choosing to arrive at non-designated airports and seaports in the area administered by Turkish Cypriots were not allowed to cross the U.N.-patrolled buffer zone to the government-controlled area in the south. Since 2004, when the Republic of Cyprus implemented new EU-related crossing regulations, U.S. citizens (and citizens of other non-EU countries not requiring visas) have been able to cross regardless of their port of entry into Cyprus.
All that doesn't give an answer to your question:
Is it possible to leave Cyprus at LCA airport without entry stamp in your passport?
If you enter the Island via Ercan, you will get no entry stamp of the Republic of Cyprus, but of the Turkish Cypriot Republic, a political entity which is not recognized as a State by the international community. (If you want to go to Greece with the same passport, you should ask to get this "illegal" stamp on a separate paper anyway.) As the Green line is not considered as a border, but only as a line of demarkation, you will get no entry stamp there for sure.
That means:
All people who can enter Cyprus with an identity card (EU and Swiss citizens) have no problems. All those who need an entry stamp in their passport, can usually cross the Green line as many times as they want and leave Cyprus from Ercan or Kyrenia, but NOT from LCA, PFO or Limassol harbour.
You will find many posts in travel forums where people tell you that the officials at LCA airport didn't check their passport carefully and that they had therefore no problem with a Turkey - Cyprus - Greek journey.
I wouldn't get this risk and just book a Ercan - IST - Malta flight (Atlasjet/Airmalta) for some 170 EUR (twice the LCA - MLA fare, I know!).
Or contact an Embassy of the Republic of Cyprus.