The incident occurred about 12.50am on Wednesday, May 19, in the Thorntonhall area, which is around two miles from Busby.
An accelerant was poured onto three cars outside the house before the blaze spread to a converted garage area which suffered substantial damage.
There were no injuries and Mr Lawwell and his family were taken to a safe location as police carried out an investigation.
Now images of a man police believe may be able to assist with their enquiries and a vehicle seen in the area around this time which they are keen to trace have been released.
Anyone who may recognise the man or the vehicle, or who has any information is asked to contact police via 101, or alternatively call Crimestoppers on 0800 555 111 in confidence.