Well yes technically I suppose so. But .45 Colt is more of an old west round like the .44-40 as opposed to the .38 spl, .357 magnum, .44 spl, .44 magnum
While not originally chambered in Winchester rifles, the .44 Russian was the father and grandfather of the .44 Magnum. The only difference, aside from using smokeless powder in the latter two rounds, was the length of the case. It was fairly common, back in the 19th Century to name cartridges, "name", long "name" and extra-long "name". So the .44 Special should have been called ".44 Long Russian", and the magnum, ".44 Extra-long Russian". I generally shoot .44-40 in both rifle and revolvers, but if I'm short of loaded .44-40, I'll change the cylinders in my OM Vaqueros and pick up a Rossi '92 both chambered in .44 Magnum. But my handloads are identical in bullet weight and muzzle velocity to the .44-40 loads, albeit the powder charges in the ".44 Extra-long Russian" (.44 Mangle-em) are
lower than the charges in the .44-40 brass due to the latter having more case capacity than the magnum brass.
One problem with using .45LC in a rifle and .44-40 in your pistols is the potential for what happened to Texas Ranger George Lloyd during a firefight with some Indians. He inadvertently loaded a .45 round into his Winchester '73. Fortunately, he was able to use his knife blade to unscrew the sideplates and remove the offending round in time to save his scalp. Had he had a Henry or '66 the outcome could have been different, as it takes about 15 minutes to remove a .45LC round from a (modern) Henry chambered in .44-40. Don't ask how I know.