Over here a number of companies produce 'lambing kits'.
This is one from the company Shearwell which I am sure they will be happy for me to reproduce.
What’s in the kit and why
Ewe spoons - You have to act quickly when your ewes suffer prolapse and the ewe spoons provides a fast, secure treatment that’s easy to apply with or without a harness.
Battles Lubricant - Indispensable. Probably the best on the market.
Castration ring applicator - It’s light and easy to use.
Castration rings - 250 rings.
Strong iodine - Disinfect all the lambs’ navels straight after birth and avoid later complications.
Tough anti-vac bottle - For feeding lambs. Boil-sterilize between uses. Ours last for years.
Non-vac teats - Pack of four. You might need more later but these will get you started.
Disposable gloves - Absolutely essential. A very popular product.
Thermometer - Keep it in the box and you’ll always be able to find it again!
Stomach tube - An essential tool for urgent colostrum needs. A real life-saver!
Lambing instrument - Safe, dependable. Never be without one.
Lamb macs 50pk - In high rainfall and cold weather, another essential addition to the kit.
Lamb colostrum - Give new-born lambs a flying start with this high energy and antibody boost.
Twin lamb drench - A pick-me-up for ewes with twin lamb symptoms. Use early for best effect.
Stomach tube + syringe- it seems scary to tube babies but it can absolutely save a lamb
Iodine
Powdered colostrum replacement or frozen colostrum
Bottle+nipples
Equipment for docking and castrating (if that's something you need to do)
Lubricant
Thermometer
Suction bulb
Propylene glycol or nutridrench
CMPK
Tiny fleece coats
A safe heat lamp or other way of warming chilled lambs
Rags/towels/puppy pads
Lamb sized ear tags or other marking equipment if you have enough lambs that you could get confused
A vet's phone number who does after hours calls
Camera for taking adorable lamb pictures