Simon Jordan also responded to the 'appalling' incident on talkSPORT and insisted issues in football 'should not be brought to someone's doorstep'.
Lawwell's family home was targeted in an alleged fire attack in the early hours of Wednesday morning, sparking a major emergency response from the local police and fire services.
It is reported attackers targeted cars parked in the driveway of the outgoing Celtic chief's Lanarkshire house, with the fire then spreading towards the building.
Lawwell and his family were forced to flee the house, which suffered 'significant damage' after an explosion and substantial blaze.
Celtic confirmed in a statement on Wednesday morning that Lawwell and his family are unharmed but 'extremely shaken and shocked', with police beginning a criminal investigation.
David Tanner, talkSPORT's Scottish football correspondent, joined the White and Jordan show to offer the latest news on the story, and said on Wednesday morning:
"It's a new low for people involved in Scottish football. We don't know who is behind it, the police are investigating and we should not speculate on that.
"But certainly, for someone's family home to be attacked in this manner is truly shocking."
Simon Jordan was also in the studio to react to the shocking scenes, with the pundit saying it's wrong to bring footballing issues and anger to where someone lives.
The former Crystal Palace owner said: "We've seen fans going outside Ed Woodward's house and doing things of a certain nature.
"Now, we don't know who these people are and the reasons for it, but we can draw the conclusions that there's a blow-back and a reaction to things that have happened with Rangers.
"But you've got people's families here, and football should not bring this to someone's doorstep.
"It shouldn't be part of someone's thinking that in any way shape or form to do something in any basis that vaguely resembles this is something that anybody can find acceptable, or even find a word to say how reprehensible it is.
"This is where a man lives! I'm looking at the footage and he's got his granddaughter and his daughter living in the property because they've all been part of a bubble.
"It's just appalling, isn't it."
"Whatever the motivations behind it, it's just appalling!"