Out of curiosity, how did this lion get in the mini van? If it lost a fight or got shot, it might not willingly walk on a leash into the van (assuming it normally, however unwisely, did so for the handler/owner). Is this a normal animal or are you writing fantasy? If the lion is out cold, then were there men on hand to drag it into the van? If it was out cold from blood loss, it died on the way to the vets, unless it was only bleeding from one limb and got a tourniquet (don't apply too tight btw)
So we have a presumably normal lion, bleeding out in the back of a van, and he's going to have to be starting to go into shock soon after he arrives at the vet, otherwise he's going to be dead pretty quick. How is your van equipped to keep an injured lion secured in the back without killing the driver? Even if he's a nice lion, in his injured state he'll likely climb over by the driver to see about getting out via the windshield and cause major issues that are not productive in getting said critter to the vet.
Next, gunpoint or no, the vet, assuming he's had even a tiny bit of exotic med teachings, is going to absolutely insist on shooting the kitteh up with some injectable anesthetics. No one in their sane mind takes an injured lion and throws him on a gurney and hopes he doesn't jump up and kill everyone in the process (even if he arrived out cold). So pissed off, half in shock kitteh (who probably doesn't look very much in shock due to adrenaline) needs to go night night. Vet is probably going to grab his drug book, look something up, guess the lion's weight, and draw up the drug or drug cocktail. You don't need to specify, but it will be whatever they use for cats only A LOT more (hopefully he has enough on hand. If you want him stressing, have him be just short the correct amount. Also, as an aside, he's going to have to explain what happened to all that controlled substance. Taking the bottles and dropping them on the floor and making up something later works. But your characters don't care, that's the vet's prob).
Okay, we've got the drug, or nearly enough of the drug. Next we have to get it in the kitteh. Unless your vet lives near a city that has the type of subculture that keeps exotics (maybe he sees a few monkeys from time to time, maybe a small zoo uses his services), he won't have a dart gun or dart pole (whatever the second is actually called, I dunno.) If the cat isn't restrained, he's going to tell the lion guy to stab the kitteh with the nasty sharp needle in the muscle. Normally he'd give quick instructions on where best to inject it. At gun point I'd say 'stick him in the ass' and hope for the best, because if I got technical, person with gun would make me do it.
Next, wait a few minutes for the drugs to take effect. Guy with gun gets impatient. Vet might mention how impossible it is to fix a lion with an arm shredded or while bleeding out in the parking lot.
Now, lion is out. Vet will check corneal reflexes really quick. Now you have to figure out how a guy with a gun, a vet, +/- a tech or two are going to get a massive cat into the hospital. Maybe they have a gurney on wheels that is low to the ground and designed for animals who can get up and down a little but can't walk well. Not likely for a guy who doesn't do orthopedic surgeries or major cases (he refers those), but maybe he happens to have one somewhere for some reason. Otherwise, up on a normal steel gurney the lion goes, and will barely fit. Either way, he's getting his arse strapped down 100 times over, and he still might kill someone if he wakes up fast. Fun, right?
And I've used up a lot of time walking through all those little details. Messing with lions is not a small matter though, and if you don't play it safe, you are screwed.
So while the lion is out, and hopefully he isn't reacting badly to the drugs due to the increasing shock, the vet and or techs are going to do a quick check for the critical stuff- level of shock (oops, worse than we thought), vitals, etc. Temp can wait until things get stitched up.
First thing to do is stop the loss (initially with a tourniquet or pressure if possible, to slow it. Then with clamps or a quick stitch. Maybe some ER docs, vets or not, could help you here.) +/- get on gas anesthesia. Gas anesthesia also helps deliver O2, which a critter in shock needs. As long as he's on O2 and the blood has stopped, things aren't totally critical, unless while doing this the critter went totally into shock. In which case we need fluids, which is what any extra hands are working on, or is what the vet is doing now that the initial stabilization is done.
They need to give proper fluids (same as a cat or dog would get for shock) to fill the blood vessels. It isn't critical that the lion get blood right away as long as it hasn't lost too much. It would help greatly if he got some very soon, because fluids aren't a perfect answer. After that, clean, stitch properly or finish stitching (depending on the wound- ie, you don't have to stitch the skin before you give fluids). The vet will give antibiotics, but might not have enough for full course of lion sized dose, but enough to get them started.
The vet may also have a specialized blood product he could get out after all the important steps are done to further assist the lion. There are 'washed' blood products that carry oxygen that are fairly universal and the only issue again is the amount the vet keeps in stock, particularly if there are other vets around and he doesn't normally see ER cases (if he normally sees none, he won't have any special products, and he won't likely have the experience or smarts to keep your cat alive)
Also, your lion can't get domestic cat blood, and your strip mall vet absolutely doesn't keep any on hand anyways. It goes bad too fast. Vets who regularly need cat blood keep blood donor cats around. So at least your vet won't be doing anything dumb by giving the lion domestic cat blood
Next, is the lion going elsewhere for further treatment, +/- blood, or what?
And now I've spent too much time at the computer. Hope that helps
