I can't imagine how difficult it is to completly avoid coconut in hair care, they put it in everthing.
I've tried different indian herbs in my hair but I have seborrheic dermatitis and they just don't clean enough.
Are you willing to use animal products? Lard is very gentle and it cures in 6 weeks vs a year. Tallow could be added to boost cleansing abilities, along with some olive oil to balance it out a little.
Wish I had a soap I could share but mine would all be cross contaminated with coconut.
Many people do use glycerin when making liquid soap but its not mandatory. It can be made with just water.
Only shikakai, areetha (soapnuts), and arappu (no English translation that I know of, or for shikakai now that I mention it) are CLEANSING herbs. I make a tea of them - the "traditional" way is to make a paste and scrub your scalp with it, then rinse it out. That is OK for pouring water over your head to rinse outside, not so great for modern plumbing. So I stick with the teas.
I've had excellent results from the conditioning herbs I've used to date. If I could get my hands on them, I'd add some other stuff like mallow root and horsetail nettle to my arsenal but by the time I knew I wanted them, any place I could buy that stuff from had either closed for covid or couldn't restock.
I am thinking of adding fenugreek to the shikakai/areetha to thicken it. Also to counteract the drying effect - even the amla/hibiscus rinse I use is very drying, and sort of terrifying the first time you do it. The first time I used it it made my hair feel all tangledy and like a briar patch on my head, but heavy conditioning and detangling in the shower followed by a detangler outside the shower while my hair was still wet worked just fine. When it dried, my hair was silky, bouncy, no flyaway, great resilience, volume and shine,stayed tangle free for days, and my curls sprang back into their full glory for the first time in decades.
Getting your hair clean with herbs can be done but its a process and unless you have allergies - much easier to stick with conventional shampoo, LOL!
I got onto the hair shtick not because of allergies (didn't know I had them yet) but because my hair had been breaking off and losing its curl for like 30 years. Turned out to be a severe protein deficiency (just in my hair) and between protein treatments (I use Neutral Protein Filler that coincidentally has no coconut content) and the Indian herbs, pretty soon I figured out there was something more going on with my scalp than just whatever shampoo of the moment wasn't "cleansing" enough. They were actually irritating my scalp due to having allergens in them. ALL of them, which is why nothing seemed to work properly. More coconut = more irritation more quickly, but they were all irritating.
I may try making the paste-type soapnut blend JUST OCCASIONALLY and applied only to my scalp with a shampoo brush to really get my scalp clean, but not on all my hair, to minimize gunk going down the drain and maximize cleaning potential.
Someday I may try making a homemade shampoo but first I have to figure out the soap thing. Burning in your nether regions is no fun and takes way longer to heal than hives and rashes elsewhere.
I'm lucky my lip balm has no coconut or palm content. I use Dr. Bronner's Naked Lip Balm. If you're not on the lookout for coconut allergens, the formulation looks very much like the Burt's Bees, yet the Burt's Bees didn't work for me and I almost didn't try the Dr. Bronner's because I already knew the similarly beeswax based Burt's Bees stuff didn't work. Now I know why - coconut content!
Lard - by "lard" I assume you mean the stuff they sell in your local bodega marked "Manteca"? That's actually mixed pork fat, not lard. No commercially sold product marked "lard" is actually lard, its all mixed pork fat (and some of it even has beef tallow added).
Sorry. Veteran baker here. Serious bakers like me search assiduously for real lard for pie crusts and it is quite expensive and hard to find. Hardly anybody raises lard hogs any more and "regular" hogs and modern breeds don't produce more than a little bit of actual lard.
Anyway I have no problem whatsoever with animal products. As long as manteca-lard doesn't have palm additives (they use them in vegetable shortening to harden it up) I'm good with it. I've been considering the use of manteca-lard since I saw it in the list of soap fats, eg - since YESTERDAY LOL! I haven't seen any coconut free recipes that use it yet. It's hard for me to figure out how to use and combine these things because every single recipe I've seen so far is either full of unobtainium (ONE recipe that used several oils/fats I can't easily get) or its 100% olive oil that takes a whole year to cure or ... the vast majority are chock-full of coconut/palm products. I don't really have a springboard to get me started.
Not sure why you have this idea that glycerin needs to be added to soap. That is not at all a requirement.
Glycerin is rarely added to bar soap (soap made with NaOH).
It is an optional ingredient sometimes used for making liquid soap (soap made with KOH). You really don't have to make liquid soap with extra glycerin, however. I often make liquid soap with just water -- no added glycerin -- and it makes perfectly fine soap.
Glycerin is sometimes used as a solvent for "transparent" and melt-and-pour soaps, but even these soaps can be and often are made with solvents other than glycerin.
That said, glycerin is naturally produced during the saponification reaction of fats. This natural glycerin content in handcrafted soap (without any added glycerin) runs about 8-10% by weight.
I don't know that it NEEDS to be added but people DO add it, especially when they want to improve trace time. Its not something that is obviously a problem for someone with my allergies unless you know how it is made. So I mention it so that people know I can't use it, and also that is why glycerin soaps are not an option for me.
Also because I have been thinking that a liquid version of a castile soap may be something I can achieve in under a year. I swear I found a recipe/process on here for doing cold process castile soap but now I can't find it. Dang me!
I also have no idea where I would get potassium hydroxide. I can get Sodium Hydroxide - Tractor supply sells 2 lbs of a pure sodium hydroxide drain cleaner for $15 (I forget the brand) - but not sure I can find potassium hydroxide.
I can't get mail so mail order is out. And if getting via Amazon, it has to be shippable to an Amazon locker, or delivered direct to my door (not a mailbox) by UPS. If USPS gets hold of it they just send it back because they won't acknowledge my disability and they now just return all my mail. It goes to a distant (for me) mail pod instead of the pod right across the street 2 doors up from my house and they will not move my box to the nearer mail pod nor give me home delivery because they say I don't LOOK disabled. And since 90% or more of all UPS shipments now go through USPS for the last leg, well. There I am. Can't mail order. And not everything on Amazon is deliverable to an Amazon locker. Just so you know. I'm limited on my shopping/shipping options. Sorry! So picky, me.