It was not possible to independently verify the claim by the Islamic Defenders Front.
Similar claims by hardline groups in Indonesia in recent years have proved to be false.
Front spokesman Soleh Mahmud said the 20 men left Indonesia five days ago and are now undergoing training in Lebanon under the supervision of Hezbollah guerillas.
The Front is mostly known for vandalizing nightclubs it considers un-Islamic or throwing stones at Western embassies. Its members have also been accused of extorting money from bar owners.
Scores of Indonesian militants fought in Afghanistan in the 1990s and more recently in the southern Philippines. Many of these fighters went on to form the nucleus of the al-Qaida-linked Jemaah Islamiyah terror network, blamed for a series of bloody bombings in recent years.
Several hard-line groups claimed to have dispatched fighters to Afghanistan and Iraq to fight the United States. Their claims were widely covering in the media, but there has been little evidence Indonesian fighters arrived in either countries.
Israel's bombardment of Lebanon has angered many people in Indonesia, the world's most populous Muslim nation. The government has said it cannot stop its citizens from traveling to Lebanon, but has urged them not to leave.
Russia has changed its position on the meeting of Russian President Vladimir Putin with his Ukrainian counterpart Volodymyr Zelensky