During her resignation speech to the nation yesterday at 1:30pm, Truss also announced that the Conservative Party's next leader will be chosen in a week's time.
Comedian Lycett, in his typically tongue in cheek manor, then tweeted at Truss: “Omg just heard there’s a leadership election nxt week????? U shud run babe youd be perfect!!!”
The comment is part of a long-running gag ever since Lycett appeared on the premiere episode of Laura Kuenssberg's politics talk show last month.
On the show, Lycett sarcastically declared his support for Truss and right wing politics.
In a moment that has since gone viral, Lycett said: “I know there’s been criticism in the Mail on Sunday today about leftie liberal wokie comedians on the BBC – I’m actually very right wing and I love it."
He then joked: “I think the haters will say we’ve had 12 years of the Tories, and that we’re sort of at the dregs of what they’ve got available, and that Liz Truss is sort of like the backwash of the available MPs. I wouldn’t say that because I’m incredibly right-wing, but some people might say that…”
Former X Factor contestants Jedward have also weighed in on the Prime Minister's departure, mocking the short length of her tenure.
The pop duo remarked: "We lasted longer on Xfactor than Liz truss as Prime Minister!"
Jedward famously lasted seven weeks on the live shows of The X Factor in 2009 before being eliminated in a sing-off against Olly Murs.
Murs has also spent as much time at number one in the UK charts as Truss has in Downing Street.
Watch below: Comedian Joe Lycett gives sarcastic response to Liz Truss's BBC interview