The chilling footage emerged as the king of Saudi Arabia warned Europe faces attack from Islamist terrorist groups in a matter of weeks unless they are faced with collective "power and speed" from the international community.
Prime Minister David Cameron and his deputy Nick Clegg will hold talks over the weekend to try to reach agreement on new measures to tackle the threat posed by Islamist extremists.
The negotiations come after the UK's terror threat level was raised from "substantial" to "severe" in response to mounting conflict in Iraq and Syria.
Cameron will make a Commons statement on Monday to propose new powers to stop would-be terrorists travelling abroad.
It comes as Labour wants more action to stop Britons being drawn to extremism.
The release of the latest video from IS comes just over a week after a video showing the beheading of American journalist James Foley caused widespread shock and revulsion. The jihadist militant group said that killing was revenge for US air strikes against its fighters in Iraq.
The Lebanese soldier, reported to be recognisable as Ali al-Sayyed, a Sunni Muslim from north Lebanon, was one of 19 soldiers captured by hardline Syrian Islamists when they seized a Lebanese border town for few days this month.
He was shown blindfolded with his hands tied behind his back, writhing and kicking the dusty ground while a militant announces he will be killed. Another militant then beheads him.
The Lebanese army declined to comment but security and Islamic State sources confirmed the latest beheading. Hours later, the group posted a second video showing nine other soldiers begging for their lives, urging their families to take to the streets in the next three days to demand the release of Islamist prisoners as a condition to escape a similar fate.
The Islamic State has been cited as a major security threat by Western governments since posting the video of the beheading of Foley.
King Abdullah of Saudi Arabia yesterday issued a warning that terrorist groups would attack Europe and the United States. While not mentioning any terrorist groups by name, his comments come in the wake of IS seizing wide areas of land across Syria and Iraq
He said that he was "certain that after a month they will reach Europe and, after another month, America".
The king's comments appeared to be aimed at drawing Washington and Nato forces into a wider fight against extremists in the region. Saudi Arabia has backed rebels fighting in Syria, but is concerned that extremists there could now turn their weapons on the kingdom.
Meanwhile, 32 UN peacekeepers were yesterday rescued from Islamist militants whohad fired on their post on the Syrian side of the Golan Heights, the United Nations said.
Another group of UN soldiers - from the Philippines - remained trapped by Islamists who surrounded their positions on Thursday, and a gun battle is ongoing. The troops are part of UNDOF, a UN force that has monitored the disengagement zone between Israel and Syria since 1974, after the 1973 Arab-Israeli war.
Around 11 UN armoured vehicles were seen returning to their base in Israeli-controlled territory about 12 hours after the peacekeepers came under fire early on Saturday morning.
"All 32 Filipino personnel from this position have been extricated and are now safe," a statement issued by the UN press office said.
The remaining troops, at a separate border post, were still under mortar and heavy machine-gun fire, it added.
"The UN peacekeepers returned fire and prevented the attackers from entering the position," it said.
Officials in the Philippines have said there were a total of 72 soldiers trapped in the area.
Another 44 UNDOF peacekeepers, from Fiji, were detained by militants around 8km (five miles) away from the Philippine troops on Thursday and remain missing.
The militants are believed to include members of the al-Nusra Front, al-Qaeda's affiliate in Syria.
The al-Nusra Front has recently seized hostages to exchange for prisoners detained in Syria and Lebanon.
The UN mission has 1223 troops from six countries: Fiji, India, Ireland, Nepal, Netherlands and the Philippines.
But the Syrian civil war, now in its fourth year, has undermined security in UNDOF's area of deployment.
Last year, UNDOF peacekeepers were held hostage on two occasions, though they were eventually released unharmed in both cases.
The Philippine government last week said it would bring home its 331 peacekeeping forces from the Golan Heights after their tour of duty ended in October amid the deteriorating security situation.
However, Fiji said it would not be pressured into withdrawing from its peacekeeping efforts in the Golan Heights.