The BBC reports he passed away at home last week after a short illness.
Following in his father's footsteps as an actor, Archie began his acting career at the Sylvia Young Theatre School at the age of 10. He first appeared as Ollie in So Awkward in 2015, and has since appeared in over 70 episodes of the popular comedy.
His other TV comedy roles include appearing in Jack Whitehall's sitcom Bad Education; playing a young version of Michael Gambon in Harry And Paul's Story Of The 2s; and appearing in 2016 sitcom pilot Our Ex-Wife.
The team at Channel X, the production company which makes So Awkward, say: "He was an incredibly talented performer and his contribution to So Awkward, on and off screen, will not be forgotten. As well as hilarious, he was a generous, kind-hearted young man who we had the honour to work with on the show for seven years. Our thoughts are with his family and friends at this time."
His friend and co-star Samuel Small, who plays Rob Edwards in the series, wrote a tribute on Instagram: "Love you from now until infinity. Rest in power bro. I wish you could've all known Archie how we knew him. I've never met someone so full of life and had touched so many people's hearts. Archie was there for me in my lowest lows but my highest highs were with him. Archie's my best friend and to say goodbye so soon is absolutely devastating, but his calling was obviously somewhere else and I hope he is brightening up wherever he is. Archie loved his friends and family so, so dearly and we hope he knows how much he truly was loved."
Sophia Dall'Aglio, Martha Fitzgerald in the comedy, shared her memories on Instagram, typing: "You were the light in the room, even on a bad day, and brought all of us together. It's true, things won't be the same without you, but while you were here you did nothing but your best to make people happy. The biggest heart I've ever known, thank you so much for changing my life in the seven years we had together. I'm so grateful."
The Daily Mail reports that police officers and paramedics were called to his family home in Fulham on 22nd September following reports of a "concern for welfare". Archie was declared dead at the scene in an "unexplained but not suspicious" death. His file has been passed to the coroner.
Series 5 of So Awkward is currently airing with a new episode scheduled to go out at 5pm today.
6pm update: Before the episode started, Newsround presenter Martin Dougan appeared in the CBBC studio to inform the channel's viewers of Lyndhurst's death. He read out a number of tributes to the actor, and explained to viewers how they could visit the CBBC website for support if they were feeling upset by the news. The episode ended with the caption "Dedicated to our dear friend Archie, with love".