It is not entirely off, but evidently also not correct.

Melanin biosynthesis is a multistep process, that indeed prominently involves the Tyrosinase (E.C.1.14.18.1) enzyme, a copper‐containing metalloenzyme that catalyzes a sequence of redox reactions: First, the hydroxylation of L-tyrosine to L‐DOPA and subsequently the oxididation to L-dopaquinone.

Since L-dopaquinone is a common precursor of both, pheomelanin and eumelanin, Tyrosinase does not explain the orange or black fur colors. It is the rate-limiting step, so gene variants with lower efficacy and expression in melanosomes will reduce the overall melanin production and thus result in lighter-colored skin & hair, both in humans and cats. A complete loss of function of the Tyrosinase causes albinism.

Without knowing anything specifically about the genetic basis of cat fur coloring, I presume that the melanocortin-1 receptor (MC1R), that is responsible for the red hair in humans, is also somehow implied in the cat. There are however other processes, e.g. the availability of cysteine, which is required for pheomelanin to form that could hyptothetically influence the balance of pheomelanin vs. eumelanin. So I would suspect something along this axis - without doubt, the orange patches are essentially only colored with pheomelanin.

Given that you can never be completely sure they're not hallucinating, large language models still seem really poorly suited for these kinds of fact-summarizing tasks.  When would you know for sure that you trust the glob of text ChatGPT gave you?  When you see citations?  That won't do because those papers may not even exist, but even if they do, the papers may not support the statement, so you have to read through them anyway.

In this case Lyon's paper does sort of exist (though two years later than what it said) but only mentions TYR within a single table in the context of brown pigmentation.  The only relevant text that even mentions calico coloration talks about sex chromosome aberrations, which makes perfect sense given what actual sources say about where the coloration comes from (for example, this book chapter mentions the X-linked aspect for "Gene O" which backs up what you originally quoted from ChatGPT) but there are no real details about calico genetics in the Lyons paper.  I also can't find the Robinson paper at all.  So, go figure, ChatGPT made a false statement with mostly fictional references with the one sort-of-reference not backing up its statement anyway.

ChatGPT is mad libs at industrial scale. The words might say something true or they might not, but keep in mind that meaning doesn't factor into how it operates at all.