Damage in LCS is wildly chaotic, and has only a few sanity checks. For example, a small handgun won't blow limbs off, and you can't instantly kill someone by shooting them in the foot. But most other outcomes are fair game -- even things like a tank barely damaging a person with its main cannon, while very unlikely, are not impossible, and the game just kind of trusts you to make sense of it.
Headshots multiply damage and permit instant kill shots, but a very low damage roll can still be shrugged off. If someone is merely nicked in the damage from a shot to the head, think of it as a grazing wound. There's blood running down their face, and their buddies are thinking it's worse than it is, but they're shrugging it off and still fighting, claiming it's nothing. In the end they get patched up and it's a scar and not much more.
Limb hits don't multiply damage and don't permit instant kill shots, but a high damage roll can still be crippling. They're especially good targets for anyone wearing mid-grade body armor, which doesn't offer protection for the arms and legs. A huge damage shot to the arm might be a bullet that punctures a major artery and shatters a bone, leaving the target bleeding badly and in debilitating pain. Even though it wasn't even their main arm, it doesn't matter -- it's bad, and they're already collapsed backward in a heap on the ground and unable to fight, maybe with the presence of mind to try to crawl to safety, maybe not.
These sorts of outcomes could probably be better sold by the game with flavor text that conveys the amount of damage done.