Street Sweeper.
Automatic shotgun that fires three round bursts.
There are two versions of the Armsel Striker. The pre-Protecta designs, and post Protecta designs. The former uses a large spring to turn the cylinder, which is wound during loading. Actual reloading of the weapon would take a lot longer than one combat round in LCS.
The latter is a pump action weapon (well, to be correct, a lever-action).
The both don't fire any quicker than a semiautomatic, so letting it have a burst is silly. The pre protecta designs had issues with the spring, so they're unreliable. The post is essentially a 12 or 7 shot pump action revolver that is slower to reload than a normal 7-shot shotgun. And heavier. And less concealable. Also they're classified as destructive devices, so C and C+ gun control laws only. And there are very few of them in the states.
No version the striker is fully-automatic. Or even semi-automatic.
There's nothing that a DAO-12 can do that a Saiga can't do better, especially since larger magazines exist, and they're more concealable/reliable, and fire quicker.
.45 SMG
An SMG that fires .45 ACP rounds, and would do more damage than the 9mm varient.
Is damage really even an issue in LCS?
STG 44
Basically an Nazi AK, it would do high damage, but be extremely inacurate.
There are not many STG-44's in the states. Liberals would have trouble finding ammo. AND they're even heavier than AK's. Also, 7.62x39 is more energetic in almost all of its loadings than the STG44. So why does LCS need the STG44?
Mauser C96
A weapon with very low damage but very high acuracy that fires 10 mm ammo.
Been playing too much fallout?
10mm is sort of a hobby cartridge. In the fallout universe, it's for some reason the most prevalent round.
In real life, it's a sort of baby magnum cartridge, more energetic in all of its loadings than 9mm or .45ACP, but not quite a .44 magnum. A hot 10mm loading is about a the weakest .44 magnum loading. Its bonus is that there are autoloaders chambered in it. Most notably, the Glock.
I don't really see a point in adding this cartridge in a C96. No C96 was ever chambered in 10mm, and I would cringe at the idea of a gunsmith taking the time and effort to ruin a historical piece such as a c96 by rechambering it. 10mm is such an energetic round that guns usually need to be designed around it, like the large frame Glocks. The first 1911's chambered in 10mm had lots of issues.
Again, there is the issue of ammo being hard to get (lots of stores don't stock 10mm), and it being hard to use. C96's are much the same: hard to find, expensive to obtain. Not worth a liberal's time, since decent 9mm and .45 ACP autoloaders, and 44Magnum revolvers exist.
IF 10mm was introduced, it should only be available at C+ to M, I think. Not quite as evil as .44 magnum, but much more "why would you ever need that you conservative?" worthy than .38 revolvers.