Lycett was known as "the resident news hound" on Josh Widdicombe's XFM radio show, which was broadcast on Saturday (and later Sunday) mornings. In September 2016, he took over from Miles Jupp as the host of It's Not What You Know, also on BBC Radio 4. In August 2013, he made his debut on Just a Minute on BBC Radio 4. In August 2011, he wrote and performed the short story "Spooky and the Van" which was broadcast in the Afternoon Reading slot on BBC Radio 4. On the radio he has been a guest on Scott Mills, Greg James and Nick Grimshaw's programmes on BBC Radio 1 and on Richard Bacon's programme on BBC Radio 5 Live.
Lycett starred as one of the contestants in the fourth series of Taskmaster, and has made several guest appearances on Sunday Brunch in the absence of one of the regular hosts. Lycett featured on Alan Davies: As Yet Untitled Christmas Special with Jason Manford, Rev Richard Coles, and Jo Joyner. He has co-written narration on ITV2 shows The Magaluf Weekender and Ibiza Weekender. Lycett has appeared on television on Live At The Apollo, 8 Out of 10 Cats, 8 Out of 10 Cats Does Countdown, Celebrity Juice, Never Mind the Buzzcocks, Spicks and Specks, Would I Lie to You?, Insert Name Here Virtually Famous, and Two Pints of Lager and a Packet of Crisps, and was a regular panelist on the E4 show Dirty Digest. He has read the Quran, and at one point told me in detail about the origins of Rastafarianism", Lycett told the Birmingham Mail in 2011. " views on race are incredibly misguided but he is very educated about it. The two became friends while touring together (with Davidson's only complaint to Lycett being that he swore too much).
Davidson is known for his offensive jokes, which have been described as both racist and homophobic, and Lycett complained about Davidson's use of the racial slur ' chink' in one of his jokes (which Davidson later removed). In his early career as a 22-year-old comedian, Lycett appeared on stage alongside Jim Davidson. In 2012, his debut stand-up show Some Lycett Hot was nominated for Best Newcomer at the Edinburgh Comedy Awards. Lycett was the 2009 Chortle Student Comedian of the Year, the winner of Bath New Act competition in 2009, the runner-up in the 2009 Laughing Horse New Act of the Year, and a finalist in the 2011 BBC New Comedy Awards. Lycett performing for the Equality Network's LGBT Rights: Stand-up for Russia event in Edinburgh, August 2013