Right, i'm at RVC and for lambing (and for uni overall) you don't need specific waterproofs. he was wearing a parlour suit, which is easier to use in the parlour and for actually lambing due to the short sleeves. He will have obtained it form uni though you can buy them on the internet cheaper. Uni didn't check our stuff so i wouldn't worry. Also, have some standard wellies for lambing as it is too tiring and a bit silly to be wearing super safetys.
it does not have to be green, that is liverpool, not RVC. At lambing time i recommend reasonably strong waterproof trousers as you spend a lot of time on your knees. Don't spend tons cos they will probably get wrecked (mine have each time i have gone lambing). Regarding a jacket i wear a long sleeved, strong berghaus (not gore-tex as it will get wrecked as above). It can be a bit annoying to have to roll the sleeves up but i find keeping drier makes up for it. Make sure the jacket and trousers have some room as it is important that you can fit a lot of layers underneath, as it has a tendency to snow (but that depends where you are in the country). The main thing i find about lambing is you have to keep warm and dry else you get miserable.