We got things such as an emergency tube feed kit and lambing ropes when we got our first sheep 26 years ago. We have never used them
For first aid and lambing, I have normal stuff like gauze, antiseptic, huggies, old clean towels, latex gloves, Lube ie farmers lubricant for assisting lambing, more huggies, 10% iodine for dipping the umbilicus (ironically in a mint sauce pot as it's just the right size
), Swiss Army Knife in my pocket, we keep a selection of antibiotics (2), syringes and needles, sharps bin, castration rings, Calciject, glucose, baby eartags (turkey wing tags for temporary marking - we put in the permanent tags at 4 months when the ears are big enough), oh and of course some more huggies. Really the huggies are probably the most important thing as they let you have relatively clean hands which prevents infection.
If you are lucky enough to have a vet nearby then you don't need much as you can call on them in an emergency, remembering it's always cheaper to take the sheep to the vet than to get a call-out.
I use an empty clean licky bucket to make up a bucket of what I will need for any particular job, so for feet: trimmers, foot spray, huggies; for lambing iodine, gloves, baby eartags, huggies, towels, lube, paper bag for rubbish and so on. We also always carry a bottle of water for us. One thing I usually forget is my glasses
Having said all that, having Primitives we very rarely actually 'lamb' ie pull a lamb. When we kept Jacobs we were forever rummaging around in them, but Hebs, Shetlands and Soay don't usually need much help. If they do of course then it often needs to be immediate.
As part of a general sheep kit we have binoculars which let you see the animal without disturbing her, and a large torch or two, always kept charged, plus we use head torches, very useful when you have no hands to spare. We both also always have a note book and pencil in a pocket, plus a phone.
This isn't a list as such. I have a cupboard which is kept locked which has medicines and all the sprays and stuff we may need for sheep. I then pick out what I will need for each situation. This works for me, whereas if I had a 'lambing box' in which was everything I possibly might need then I would waste time fossicking in it to find what I need. People who keep sheep far away from their home often have the equivalent of my cupboard in a large box in their pickup so they won't have to go home for what they've forgotten.