I've actually been ruminating on our next god having some music-related thematics.
Category being Maker/Builder/Crafter is fairly obvious, to supercharge the rest of our construction and up-tech efforts, and Domain being Bees is also fairly obvious, both because bees also build structures and because black-and-yellow ties in with the use of obsinite and gold in the things Lizardmen make. But that still leaves the Variety of the god, the concept that goes in between the high-level Category and the more aesthetic Domain.
What I hit on for that, for maximum utility and appropriateness, was Harmony - both the arrangement of things in harmony (components of a device, individuals in a team/society, buildings in a city, cities on a planet, and so on) and the benefits of doing so (a device functioning because it is assembled correctly, many individuals working together accomplishing more than the sum of what they could working alone, civic planning improving the efficiency and quality of life of those living and working in a city, and most of all the power of the geomantic/astromantic web that arises from everything being arranged just right).
Between bees communicating with dance and Harmony also having a musical meaning, the rest of the characterization arose naturally - a god in constant motion, a never-ending dance of construction, assembly, and craftwork. It's hard to say whether they appear as many lizardmen at once or as one lizardman with many arms, all holding a different tool or work-in-progress and working in synchronicity, the sounds of their work a symphony; it's hard to say exactly which breed of Lizardman they are, and a non-lizardman viewer might not even perceive them as a lizardman at all; it's hard to say whether they are made of obsinite decorated with gold or made of gold decorated with obsinite, but their eyes are honey-golden amber and shine with a warm light either way; and, always, there are bees there with them, buzzing in tune with the music that drives them, aiding them in their dance of creation.
No cripple chained to their anvil, no bitter slave are they - they are the state of Flow personified, they are a labor-buddha, they are the principal of "if you do what you love you will never work a day in your life", they are sweet and joyful! They are rewarding work, both in the sense of rewards produced by work and in the sense of work being rewarding in and of itself. They are a cheerful, friendly, ray-of-sunshine of a divinity. And they will happily sweep you into their mesmerizing dance, and share both their work and the products of it - greatest of those rewards being the capacity to work on new things.
And for those who would disrupt and destroy the harmony of their crafting, or try to steal the benefits of it without contributing to it? They get the bees. (In other words, Favored Foes would be vandals/saboteurs and parasites.) But combat isn't really their role so they generally either try to get the problem being to start dancing to their tune along with them, thus ceasing to be a problem, or they drive the troublemaker off with ohnonottheBEEEEEES and let them get lost in Ayotzl's mists or get their face bitten off by Sotek or [insert action by appropriate other god here].
Watching them at work is kind of like watching one of those almost hypnotic videos of things being built by an automated assembly line where things don't ever hold still, things just move forward to the next step while whatever just got done is seamlessly repeated for the next thing behind it - except it's very hard to just watch, you feel yourself starting to move to the beat of things... and then a few hours later you snap out of it, and you're in a building or water/air/void-craft with a pile of useful equipment and a jug of mead and/or box of honey-based edibles, you're aware that you helped make all of these things, and you and everyone else there is totally psyched up for the next big project.
The method of worship is, obviously, constructive work, but if you want something more symbolic, there are working songs and dances, and there is the sharing of mead and/or other honey-based foodstuffs that (and this next bit is important) all of those sharing them worked together to make. Blessings would come in the form of intuitive understanding of how to arrange/coordinate things for maximum effectiveness, awareness of where something is missing/broken or being disrupted that needs to be repaired for things to work properly (either in practice or in a design), magic music that helps everything and everyone just fall into place (everyone knows the right action to take as if it was the next step of a familiar dance, everything they need is in just the right spot when they need it because that's where it was left earlier in the dance or because a bee showed up and nudged things or because reality just bent a little to make it so), extra power to/from the geomantic/astromantic web, or (in an emergency) the summoning of a swarm of angry BEEEEEES! (Bees. My god.) Also tirelessness, but that's usually redundant for Lizardmen.
If Vaul ever meets them, it'll be, like, he wants to be totally jelly, but they're just so nice and then they just dance into his workshop, and one musical montage later all the work Khaine's dumped on him this time is done and there's actually time left over to work on something he wants to make instead of another bloody weapon for once... Meanwhile Cegorach is like "wow, it's like if me and the smith had a bee-lizard baby" and he'd probably get along with them for a while, but a deity produced by the blunt and literal-minded meat robots that are the Lizardmen is probably going to miss the point of a lot of jokes and eventually their natural cheeriness won't entirely make up for that, so the clown will try some kind of mischief and end up having to Exit, pursued by BEEEEEES.
For a name, I'm less certain - maybe Itoti, from itotia/ihtotia (nahuatl word meaning to dance or to get someone to dance) except symmetrical.
Symbols are of course bees and honeycomb, and maybe also interlocking gears.