Sthomper,
People are attempting to help you.
You're using confusing terminology.
A lever-action can quite easily function with rimmed cartridges, whether straight-walled or bottlenecked.
Marlin, Winchester, Ruger, Rossi, Henry, Uberti and others have all made leverguns that shoot them.
Marlin has produced guns in .357/.38, .44 Special, .44 Mag, and .45 Colt for many years. The .45-70 is also a rimmed cartridge that's been used in leverguns for well over a hundred years.
How do the guns do it with a rimmed case? They just do, it's what they were designed to do.
A "modern" levergun is just a current levergun. The 1894C is a modern gun.
I'm aware of only two current leverguns that "stack" cartridges vertically, the Browning BLR with its detachable box mag & the Winchester Model 95 with its integral mag. May be more, but they don't come to mind. (The old Savage had a removable magazine, no longer in production.) In others they either sit horizontally in a line under & parallel to the barrel, or in the discontinued Ruger levergun they ride in a rotary magazine.
Stacking, to me, implies a magazine like the Browning, an AR-15 or 1911 pistol uses. Dunno what you mean by "stacked on top".
Does a lever-action take a rimmed cartridge in some way that a carbine can't?
What do you mean?
There are loads of lever-action carbines out there, many that fire the .357/.38, and the little .357/.38 Marlin is one of them.
If you're thinking a carbine is only an M1, or only a gun that takes a removable box magazine, you've confused yourself and me along with it.
Your apparent definition of a "carbine" as a "magazine rifle" is vague, contradictory & meaningless. A removable magazine is not a criterion in defining what's a carbine & what's not a carbine. As has been said above, a magazine is simply a device for storing & feeding ammunition, and the underbarrel tube is a magazine.
There are lever-action carbines, there are semi-auto carbines, there are bolt-action carbines.
There's no point in you getting indignant with people trying to answer your questions when you can't use the correct terminology.
Yes- the Marlin can fire both .357 and .38, as you've been told.
How it does it is simply a matter of it being designed to do it.
Denis