The Cat Lord is not a deity
Until the 5th Edition Volo's Guide to Monsters, none of the many variations of "Cat Lord" in D&D canon rose past rank 0 "quasi-deity," and even that was only a sidebar'd suggestion in the Epic Level Handbook.
In terms of religious veneration of the Cat Lord, the best attestation I could find came from Dragon Magazine Compendium, in which the tibbits are also said to follow the Cat Lord. Here, the Cat Lord is identified merely as "a powerful creature" and it's noted that the tibbits have no organized religion surrounding her, viewing her as more of an older brother figure and spiritual protector. This includes no details about any religious practices.
...but the tabaxi have other gods
The gods of the tabaxi, at least in the Maztica setting, are Tezca, Nula, Azul, and Zaltec.
Tezca is a chaotic evil solar deity. He desired fresh human hearts as sacrifices. His faith is a brutal one; each day at sunset, his priests congregate to offer the fresh heart of an unfortunate victim to ensure that the sun-god shall show his face again tomorrow. His faith is related to warmth, life, and power over fire.
Nula is a chaotic neutral goddess of wild beasts, a demipower whose influence is growing slowly across the Maztican continent. She is invoked by hunters and those who fish, leaving gifts of seed and bone in the wilds for her to know she has been called upon. Primarily depicted as a monkey, she has lesser aspects representing many other animals of the wilds.
Azul is a lawful evil god of water and rain. Often the first deity enshrined and venerated in new territory (to ensure the rains favor this land and will provide for its people), Azul watches over all bodies of water, from the smallest streams to the mighty ocean, and even the very rare (in tabaxi territories) snowfalls. His priesthood keep themselves scrupulously clean with baths and pumice stones. Foul sacrifices are performed to him in the spring to ensure a prosperous wet season.
Zaltec is a chaotic evil war god, a vicious deity symbolized by skulls, hearts, blood, and jaguars. Tabaxi who have fallen under the sway of a tabaxi lord (a related creature) tend to worship Zaltec. He is venerated by fresh hearts on his altar, blood spilled in battle, fasting, and ritual scarification. His priests wear black robes, wash their hair in the blood of their victims, and spike it outward in garish diplays. What that might look like, who could say.
Beyond that, though, there is nothing official about the Cat Lord's religion
...because, as noted above, it simply doesn't exist. "Cat Lord" is a well-worn trope in D&D, having appeared in some form in short stories (a group of them appear), novels, the 1st Edition Monster Manual II (the original, a male), Planescape (the second, a female), the Epic Level Handbook (a 37th-level shapeshifting rogue, male) and elsewhere on and off. Until Volo's Guide, however, none firmly attributed deity status to a Cat Lord, and no source that I've found suggests any kind of open worship.
That doesn't mean you can't borrow some...
There are other feline deities, of course - you can look into Ferrix, goddess of weretigers; Bast, a vengeful Egyptian tutelary cat goddess, and Sharess, a Faerunian demipower of cats and hedonism. Any of these might provide a reasonable model for a Cat Lord religion, if that's what you're after.
I hope this has helped.
Role playing came out of wargaming, virtually all of which used miniatures. Chainmail was just one of hundreds of miniature-driven wargames, mostly historical military in nature. Sci-fi and fantasy wargames became popular in the 1960s and 1970s, especially in the wake of the popularity of The Lord of the Rings, so there were many products to choose from.
In fact, at the time, wargame rules tended to spring up around miniature products and not vice versa. Gary Gygax originally became interested in 40mm Elastolin miniatures in the late 1960s and participated in writing various historical wargames to use them prior to Chainmail. A detailed account of this evolution is available in the Chainmail Wikipedia entry.
Best Answer
I know that Citadel/Games Workshop produced 28mm pewter Lord of the Rings miniatures years ago for MERP (a complete list is available on solelegends.com. Those are out of production, unfortunately; they still produce Lord of the Rings miniatures for their own tabletop battle game, but 25mm and in plastic, like most of their miniatures now, and they also have their strategy battle universe, which has 10mm miniatures fit for more epic battles.
Mithril miniatures also produces miniatures for MERP, though unfortunately, in 32mm scale and 54mm scale.
Mithril Miniatures was predated in their license by Grenadier in 1985, a now defunct miniatures company that produced a licensed Lord of the Rings miniature line. They transferred their license to Mithril in 1987. (1)
I think those are/were the only choices for official Lord of the Rings/MERP miniature lines.