I respectfully disagree.
While Ms. Lansbury never got the chance to play film roles she was able to play on stage and TV, but it doesn't mean her film career is unworthy of an Honorary Oscar.
Yes, she a the queen of Broadway and TV icon, but she's also one of the greatest character actresses in Hollywood history with over 50 film credits under her belt.
She's been nominated for an Oscar on three occasions, not twice. And God knows she should've won for The Manchurian Candidate (1962) - Patty Duke's win has to be one of the biggest upsets in Best Supporting Actress category considering that Lansbury was thought to be a shoo-in for the win and won both the Golden Globe and the NBR Award that year.
Her first two consecutive Oscar nominations made her the youngest 2-time Oscar nominee ever - a record she still holds 70 years later.
In addition to her Oscar nominated work Ms. Lansbury gave us a plethora of great performances in such classics like The Harvey Girls (1946), Frank Capra's State of the Union (194

, Cecil B. DeMille's Samson and Delilah (1949), The Court Jester (1955), The Long, Hot Summer (195

, The Dark at the Top of the Stairs (1960), All Fall Down (1962), The World of Henry Orient (1964), Bedknobs and Broomsticks (1971), Death on the Nile (197

. Not to mention her voiceover work in The Last Unicorn, Beauty and the Beast, Anastasia.
She was also excellent in Harold Prince's cult classic Something for Everyone (1970), The Company of Wolves (1984) and musical The Pirates of Penzance (1983).
Her theater and TV work may eclipse her film career, but she shouldn't be punished for achieving great success in all 3 mediums.
After all both Eli Wallach and James Earl Jones had far more impressive careers on stage than in film, but it didn't stop the Academy from presenting them with an Honorary Oscar in in 2010 and 2011.
Bonus track: Angela Lansbury sings Open a New Window at the 1971 Tony Awards:
https://www.youtube.com/watch?v=iM6jvMXzcPk (I wish it was It's Today or If He Walked Into My Lifeinstead)