The pair originally argued when former newspaper editor Piers tried to get Allen to appear on his new US talk show, and this time the contentious topic was The X-Factor.
Lily Tweeted: 'Nice to know that i'm 80% confirmed to be a judge on xfactor, anyone thinking about running it by me ? (sic).'
Morgan responded: 'Did Bianca Gascoigne turn it down then?'
Allen retorted: 'Don't be a snob Piers, it doesn't suit you, oh wait a minute................carry on !'
Morgan then said: ''Laughter would be bereaved if snobbery died'. - Peter Ustinov. Anyway, if you need some tips on how to be a talent judge, you know where to find me. (Answer: Hollywood).'
Allen retorted: 'YOU ARE SUCH A D**K !!!!!!!!!!!!!!!!'
Morgan responded: 'I can always tell when I've got you riled, you start using capital letters. I'm off for a bike ride now, do try and calm down by the time I return....'