Three other people have already been sentenced to death for espionage.
The spying investigation has particularly unnerved Hezbollah, which fought a two-month war with Israeli forces in 2006.
One of the men sentenced to death this month, Hassan Ahmed al-Hussein, was convicted of giving Israel the names and addresses of Hezbollah officials in the southern village of Qantara.
Another man, Ali Manstash, was given the death penalty last week for giving Israel the locations of military targets during the 2006 war.
Hassan Nasrallah, the leader of Hezbollah, claimed earlier this month that Israel has “complete control” over Lebanon’s telecommunications infrastructure.
He suggested that Israel would try to plant evidence to influence the Special Tribunal for Lebanon, the United Nations panel investigating the assassination of Rafiq al-Hariri, Lebanon’s former prime minister.
Al-Hariri’s supporters, meanwhile, have accused Hezbollah of trying to interfere with the tribunal.
Nasrallah is expected to hold a press conference at 8:30pm Beirut time (17:30 GMT) on Thursday. Hezbollah has promised a “major announcement,” but the group has not revealed any details.