Did Israel give Lebanon full and fair warning of attacks ?

I keep a stack of old newsprint beside my bed to use to catch my whiskers when I trim my beard.

The other day, as I was tearing off the top few pages of newsprint for this purpose, I casually looked down and the article caught my eye. It happened to be the June 2nd edition of the Jewish Chronicle. The news report was written by Joseph Millis, Foreign Editor of the paper. It's on page 9 . As I quote from that article bear in mind that the Israeli onslaught on Lebanon did not happen until July 12th:

"Israel this week warned Lebanon that the country would pay a "heavy price" if it allowed Hezbollah to continue to operate from the south of the country. The warning-- issued by a top military commander -- came after Israel responded with air strikes to a Katyusha rocket attack across the border on Sunday. (...) One of the rockets hit an Israeli Air Force installation on Mount Meiron, near Safed. "We hope the message from our response [on Sunday] was understood correctly by the other side", Brigadier-General Gal Hirsch, the commander of the Galilee division, told reporters on Monday. (....) The fighting ended on Sunday afternoon after the Lebanese government requested via the UN a cease-fire with Israel. On Monday, senior officers revealed that prior to the Lebanese cease-fire request, Israel had threatened to bomb additional parts of Lebanon, including Beirut, and not just the southern part of the country controlled by Hezbollah. "We told them that we would expand our firing to other parts of the country", one senior officer told the Jerusalem Post. "they understood very well what we meant". Last Wednesday - the [sixth] anniversary [of Israel's withdrawal from Lebanon] - the pro-Syrian Lebanese President Emile Lahoud praised Hezbollah, saying it should "stay[ in place] until a just and comprehensive peace is achieved in the region". However, Lebanese Christian, Sunni Muslim and Druze groups were less enthusiastic about Hezbollah "Firing rockets from South Lebanon is a violation of Lebanese sovereignty," the anti-Syrian March 14 Forces executive committee said in a statement. "There is a serious security vacuum in the area due to the lack of the government's control." [The group's] leaders include include Sa'ad Hariri, the son of assassinated former Prime Minister Rafiq Hariri, and Walid Jumblatt, the Druze leader.