Born in Levadia, he joined the Orlov Revolt in 1770, but not pleased by the result he built up a small fleet and began harassing the Ottomans in the Aegean Sea. In 1778 he assembled a Greek pirate fleet of seventy vessels, which harassed the Turkish squadrons in the Aegean and forced the Ottomans to abandon the island of Kastelorizo; the castle on the island was renamed to Lambros Katsonis Castle. In 1790 he engaged the Turkish fleet in Kafirea, defeating it. Katsonis had his hideout in the bay of Porto Kagio. His crew grew very restless and they attacked and sunk two French naval ships. This caused the French to join with the Ottomans to try to stop Katsonis. They cornered him at Porto Kagio and Katsonis' navy was destroyed. Katsonis escaped to Odessa and Yalta where he was granted the Livadia estate —what was later to become the Livadia Palace estate— by Catherine the Great. He lived out the rest of his days there.
His wife was known as Angelina in Russia, but her real name was Maria Sophianou. He had three sons and possibly one daughter. His first son was killed by the Turks when was still infant, in the Greek island of Kea. The second, Lykourgos (known in Russia as Ликург Ламбрович Качиони, 1790-1863), born on a Greek island, had a brilliant career as officer in the Russian Army, including his service in the Greek Battalion of Balaklava. The third son, Alexander who was born in the Crimea, also became an officer in the Russian Army. According to some sources he had a daughter named Garyfallia, but there is no information about her life. One of Lambros' grandsons, Spyridon son of Alexander, was a known Russian writer. He was also the godfather of Odysseas Androutsos, a commander of the Greek War of Independence. He died in Crimea.
The Livadia Palace, the summer home of the last Tsars was built on Katsonis' Livadia estate after 1861. The name of the estate was given to it by Katsonis, who named it after his birthplace; moreover, this is the origin of the name of Livadiya town itself.