The source said two of the soldiers died in Tuesday attack, which occurred near the town of Arsal, while a third died later in hospital.
The border areas around Arsal are used by Syrian rebels battling President Bashar al-Assad to smuggle weapons and fighters from Lebanon across into Syria, and the region has seen previous clashes between the Lebanese military and Syrian fighters.
In February, four Lebanese soldiers and two fighters were killed in a gun battle near Arsal.
The latest shooting comes as an assault by Syrian soldiers, backed by Lebanon’s armed group Hezbollah, continues on the nearby Syrian border town of Qusayr to drive out rebels.
On Sunday, two rockets hit the Shiyah district in the southern part of Beirut, Lebanon’s capital, wounding at least five people.
Shiyah is a stronghold of the mainly Shia Hezbollah, whose leader Hassan Nasrallah confirmed on Saturday that his fighters were directly involved in Syria’s conflict.
Nasrallah pledged in a speech that his group, which is backed by Iran, would turn the tide of the conflict in Assad’s favour, and stay as long as necessary to do so.
The fighting in Syria has already spilled over into Lebanon’s second city, the northern port of Tripoli, where 31 people have been killed and 212 wounded in a week of clashes between pro-Assad Alawites and pro-rebel Sunni Muslims.
Update 1: Security source told LBCI: The soldiers’ checkpoint in Arsal was stormed with a Hummer, their arms were seized, they were beaten up and shot in the head.
Update 2: Ali Hujairi, the municipal chief of Arsal, told Voice of Lebanon radio that the city’s residents were not involved in the attack. He added some of the townsfolk pursued the attacker’s Hummer before it crossed the Syrian border.
Update 3: The Lebanese army command said the three soldiers were killed in Arsal during a gunfight with the assailants. The military is carrying out a largescale search operation.
Update 4 : LBCI reported that Caretaker PM Najib Miqati telephoned Army chief Gen. Jean Qahwaji to discuss with him the deadly attack on soldiers in Arsal.
Update 5: Outgoing Prime Minister Najib Mikati wrote via “Twitter”: “The Lebanese are united around the Lebanese army specially during these difficult circumstances experienced by our country.”
Update 6: The Lebanese army reinforces deployment at all the entrances of the town of Arsal near the border with Syria
Update 7: State Commissioner to the Military Court Judge Saqr Saqr tasked the army intelligence and the military police with carrying out the initial investigation into the shooting on the 3 soldiers in Arsal.
Update 8: Lebanese Forces leader Samir Geagea condemned the attack against the army in Arsal, urging against exploiting the incident for petty political interests.
Update 9: Grand Mufti Sheikh Mohammed Rashid Qabbani also condemned the attack against the army in Arsal:” The daily security incidents are aimed at creating strife and chaos in Lebanon”, he said.
Update 10: Prime Minister-designate Tammam Salam condemned the attack against the Lebanese Armed Forces .
“This is a condemnable act perpetrated by cowardly criminals,” Salam said in a statement on Tuesday.
Update 11:President Michel Suleiman called for punishing those who attack the army and security forces.
“Those who permit themselves to attack the army or the security forces should be struck with an iron fist,”
Suleiman was quoted as saying by the National News Agency
Update 12: Former Lebanese president and Phalange Party leader Amin Gemayel denounced the attack against the army in Arsal, describing it as an “attempt to dirupt the role of the military and to intimidate it.”
Update 13 : LBC reported on Thursday that two people were arrested in connection with the attack against Lebanese army in Arsal.
Update 14: PSP Chief MP Walid Jumblatt denounced the attack against the army in Arsal during talks with Army Commander Gen. Kahwaji: “We support the military and the efforts exerted by it to maintain the civil peace, ” Jumblatt said on Thursday