Generally Lesvos appropriate for any fishing. Surely you must have a car or bike and the best course, a small boat.
Fishing out the best areas are in Agrilia (south of Mytilene 12Km) in Tsonia (40Km) in Molyvos (60Km) and Sigri (98Km). If you have a boat try Myrsini near the entrance of the Gulf of Gera, the Toukmakia, the reef of the porbeagle in the north of the island, Gavathas, the islets of Sigri, the Myrmigki in Tavari, and fishing within it often offers enough thrills .
Bait can be found in fishermen (shrimp and frozen horse mackerel) but also in fishing shops where you can find live bait (worms, bug, pharaoh etc). Also for long trips are two pagopoieia near the city in a gravel one in there.
For snorkeling the best areas are from Molyvos by Sigri with any fish. The Gulf of Kalloni is ideal for fishing the famous Kalloni sardines, Languages, pandora, murmurer, heads and shells.