I think the obsession with dry food comes from people believing it helps clean the cat's teeth. Perhaps it might - if they chew it. Some cats just swallow it whole (mine do!). The problem with dry food is that cats have a low thirst drive, and usually get most of their water from the food they eat. If you feed them dry food, they will increase their water drinking slightly, but not enough to make up the loss. This is believed to be why so many older cats are get urinary tract disease and renal failure. Dry food usually also has a lot of carbs and veggies in it that cats simply don't need, and comes out a stinking mess in the litterbox.
I had a glance at the Lily's kitchen stuff, it looks like its really high-quality stuff. Were your cats exclusively eating this or did they still have access to dry? I haven't ever fed mine tinned (one of my cats wont touch the stuff, annoyingly) so I don't know what poo is like when cats are on it but I would have assumed, if a quality tinned, it would be much better than if they were on dry.
Yep I feed raw meat, a mix chicken and lamb usually. You need a mixture of meat, organs, and bone for it to be a complete diet. It's just stuff I buy during my weekly shop, I chop it all up and put in tupperware in the freezer and voila a week's worth of incredibly high quality cat food. I got my recipe from here. My cats actually do chew this food, unlike the dry, and the bones get a good crunching! You can also buy pre-made raw online to pop into your freezer, but I do not have the freezer space to order this myself.
I do also give a little bit of dry food every few days in toy, just as a bit of variety and something to play with. I use Applaws dry now that I've run out of RC because that has a 80% meat content.
Anyway, lots to think about when feeding your cat. I think there is loads of confusion regarding feline nutrition, but I concluded I was just going to feed them the closest thing that matched what they would eat in the wild, which is meat.