The question was over whether the Caspian was a sea or a lake.
But if it is defined as a lake, then it could be divided equally between all five countries.
From an energy perspective, Iran would be a natural market for the Caspian basin's oil and gas, as Iran's major cities (Tehran, Tabriz, and Mashhad) are closer to the Caspian than they are to Iran's major oil and gas fields.
Purchasing energy from the Caspian would also allow Iran to export more of its own oil and gas, making the country a transit route from the Caspian basin to world markets.
Iran could earn fees for swap arrangements or for providing a transit route and justify its trade with Turkey and Turkmenistan as the swap deal is allowed under the Iran-Libya Sanctions Act (ILSA, or the D'Amato Act).