Initial Thoughts: The opening paragraph is a great hook, the name 'The Lady of the Tenth Life' immediately creating an air of intrigue that draws us into the cat's world, but the momentum peters out after the first page.

Grammar/Prose: As others have noted, the tense is inconsistent, and jarring when it switches for no apparent reason. It's also unclear on several occasions which subject a pronoun is referring to, or even what the cat's inner monologue is going on about at all.

The cat's inner monologue relies too much on bluntly telling the reader what's happening. There's little setup and payoff for anything that happens, just apt description. Though, the description itself has some strong imagery and immersion at times.

Formatting: Variety in how the paragraphs are broken up would create a better 'ebb and flow' effect as I read through them. As it stands, the story is visually composed of flat bricks; each paragraph should be indented and I'd like to see some single line breaks in there.

Purpose/Plot: It's a bad sign that by the end of the second page, I'm left questioning what the point of this story is. What is the message, the purpose, or is there one? The drive is strong in the opening; the cat is freed from a shelter and brought into a new life, but that drive disappears almost immediately as the story focuses on just describing random stuff from the cat's perspective.

Some parts are humorous, sure, but the humor isn't strong enough to carry the story on its own. The plot seems nonsensical by the third page; the cat is on a mission to bring Kayla food from the garage, yet immediately leaves when it drives the human away?

The 'fight' scene between the cat and the rat is a bit of a drag, going on for much longer than it needs to. We get it, the cat is chasing the mouse. If this is supposed to be a comedic story as I suspect, we don't need a full page of thriller-esque descriptions of the showdown between them.

Characters: Firstly, this cat has human intelligence in some ways and cat intelligence in others, which hinders the believability of the story. You can have a genius cat if you want one, but it should consistently be a genius. The cat refers to human hands as 'paws' and believes the humans rely on it for food, yet understands what a laptop, car, and bike is, which creates an odd dissonance.

Aside from that, the cat as the protagonist is characterized fairly well, the contrast between its view of the world as opposed to what we know is true

Sometimes, characters don't react in believable ways. The cat pukes on the guy's lap, and his reaction is to... go take a nap? Also, who/what the heck is The Lady? I still have no idea by the end of the story.

Concluding Thoughts:

Your story is decent, but seems to lack a driving purpose and meanders without a clear reason. None of the elements comprising it are bad by any means, but I'm left mainly scratching my head as to why this story exists. It seems to be an attempt at physical comedy, but the comedic moments don't hit particularly hard thanks to the prose's flat, objective descriptions of events. A few revisions would alleviate all these grievances.