But the moggy is unable to respond to the invitation to enrol - he is missing.
Ms Lyes tweeted that she hoped the exposure would help to bring Chairman Meow back home.
She said she was surprised at the popularity of her post about the "bizarre" letter.
"Cats just get a good run on social media, I guess, and to see people around the world posting about this weird letter to my cat is pretty funny.
"I've had a lot of good feedback. Some people have even asked to use his name, which is great - share the love, I say."
She hopes Chairman Meow's newfound fame will help to convince him to return home, although she suspects he may be living up to his political namesake.
"He's probably just rounding up other cats or stockpiling food for the big revolution, I'm sure."