LCS Humans have the following parts: Head, Torso, 2 Arms, 2 Legs, Upper Spine, Lower Spine, 2 Eyes, Tongue, Face, Heart, Spleen, Liver, and 32 Teeth.
There is also the lung.
But when either side collapses your pretty much done for.
Not if you can get to a hospital. It's an emergency that forces you to seek professional medical treatment, but it's nowhere near as bad as a wound to the heart. And first aid can stabilize long enough to get the Liberal offsite. (Which is sufficiently realistic. In real life a punctured lung is an emergency, but is quite survivable if you can get to a hospital.)
Oh, and LCS humans also have ribs...
Actually, there's an idea: What about a clinic (complete with makeshift operating room) as a safehouse improvement? Call the first aid skill "Medical", and let Liberals recover from serious injuries in the safehouse if they have a doctor with medical skill present. The check need only be made once, on the first day--if there's a doctor there to do the necessary surgery, then after that the patient is stable and can recover on their own (faster with treatment as usual). If nobody present has Medical skill, or the safehouse has no clinic, the Liberal is forced to go to the hospital or die. If the doctor fails their Medical check, the patient goes down a level in wounds, or if at near-death, dies. A botch could also result in a reduction in Health attribute for the patient, but you'd have to go easy on that because of how often LCS characters get hurt. Botched treatment for damaged appendages could result in an amputation.
The benefit of this would be that Liberals who are injured and go to the hospital can now be arrested without it being game-breakingly frustrating to have a Liberal arrested every time you put him in the clinic for medical care. I mean, realistically, what do you expect--Somebody shoots up a latte stand; twenty minutes later, a guy with a bullet in his kidney gets dropped off in the emergency room by a bunch of guys whose car just got described as having been in a police chase with a bunch of death squad officers. That's REALLY suspicious there. Should be an automatic arrest. Heck, I used to get my founder deliberately punched in the face a couple times just so I could check him into the clinic and avoid him catching a lucky bullet in an inevitable siege, or else provoking an inevitable siege before I was ready, because he had a few hundred murders under his belt. That kind of exploit shouldn't be possible.
A sleeper at the hospital should reduce the chances of arrest, though. For multiple high-effectiveness sleepers, it could be essentially zero.