At around 12.25am on March 9, a light coloured Vauxhall Astra car pulled up in Grimshaw Lane, police say.
A male passenger then left the vehicle, ran across a pub car park and approached the driveway of a property in Yew Tree Road.
Footage shows the man pouring accelerant over the bonnet of a Volkswagen car and setting fire to it before he returned to the Vauxhall and made off from the scene.
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The front of the vehicle was destroyed, with heat from the blaze damaging a Citroen car parked on the driveway, say police.
Fire crews attended the scene and the fire was quickly extinguished.
Two children who were in the property at the time of the attack are said to be "upset" and "shaken up" by the incident that happened in Ormskirk.
Detectives are now appealing for information and are particularly keen to speak to anyone who recognises this man in connection with their enquiries.
Det Sgt Stephen Monk, of Lancashire Police, said: “We have launched an investigation following an arson attack at an address in Ormskirk.
“The occupants, including two children, were inside at the time of the fire and have been left extremely upset and shaken up by this incident.
“We believe this is an isolated attack and are particularly keen to speak to this individual, pictured. He has a distinctive run and we believe someone may know who it is.
“Following enquiries, we believe the vehicle used by the offender is a light coloured Vauxhall Astra registered between 1998 and 2001. If you saw this vehicle, or anyone acting suspiciously in the area around the time of the offence, please contact us.”
Nobody was injured during the incident.
Anyone with information can contact police on 101 quoting crime reference SB1700895.
Alternatively, Crimestoppers can be contacted on 0800 555111 or online at www.crimestoppers-uk.org.