Viewers were left confused after Lycett walked off the daily talk show, which is based in Leeds Dock, on Thursday, July 1.
Earlier in the show, the Birmingham-born comedian had discussed giving up single-use plastic to help the environment.
However, when discussing Love Island later in the show, McGovern showed a picture of Lycett sat in his garden, saying he had "pimped" up his garden to make it look "more Love Island".
The presenter then pointed out a single-use plastic bottle in the photo.
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She said: “Isn’t that one of the bottles you said you’d stopped using, in that picture?" to which Lycett responded: "I didn't realise I was on Newsnight, Steph".
Joe was then seen on camera removing his microphone and walking of the live set.
When the show returned from the ad break, McGovern said: "Joe Lycett was going to stick with us but he's had to leave."
However, Lycett today confirmed that the whole thing was pre-arranged.
In a statement, he said: "Some of you might’ve seen or read that I had a ‘tantrum’ on Steph’s Packed Lunch yesterday and ‘stormed off’ the show. This is absolutely true. What you might not know is: I planned the whole thing.
"Clear PET plastic bottles are widely recycled and contribute to the circular economy.
"If you put a clear PET plastic bottle in the recycling there’s a good chance it will become another clear PET plastic bottle. Coloured and in particular white PET plastic bottles are much harder to recycle.
I explained this on Thursday’s show, but later a picture with a bottle (made with white PET plastic) appeared on screen.
"Steph pointed out my apparent hypocrisy and I KICKED OFF (by ‘KICKED OFF’ I mean ‘took my mic off and left the studio’).
"All of it was planned, all of it rehearsed. Today I seeded pictures of me drinking from one of these bottles which Greg James agreed to retweet.
"The tabloids loved it - Mummy’s all over the press!
"The bottle in question? Yop.
"I risked my reputation as a jolly, affable and very-much-available chat show guest to say this as loud as I can: Yop, it’s time to stop using white PET plastic.
"What you sayin’ Yop?"