The British Lee rifles were never intended for any round other than .303. A .402 round was designed exclusively for the new MkIV Martini-Henry, but never issued when it was discovered to be, although about the best of its kind, obsolete following the development of "chemical powder" by the French. This instantly killed off the impracticality of much smaller calibres, of which the advantages were well known.
The .303 was never intended as a black powder rifle. An Explosives Committee already had samples of the French Poudre B and Nobel's Ballistite, but considered improvement to be required in either case. The black powder pellet, long since found inadequately accurate in the ..577 Snider, was only a stopgap, and the issue Lee-Metford sights were calibrated for a slightly higher velocity than it would produce.
The British government's powder, which appeared in only two or three years, was cordite, and another myth is that the rounded rifling o the Lee-Metford was unsuitable for smokeless powder. It was true of the original cordite, with a 58% nitroglycerin content, such as nowadays is found only in solid fuel rocket propellants, since you don't get your nozzle back after their single flight. The segmental Lee-Enfield rifling was a very incomplete solution, and very early in the twentieth century it was reduced to 30%, which itself is more than modern double based rifle powders. Moderate use of smokeless in an original Lee-Metford is about as acceptable as in any collectible rifle.
There were indeed plenty of .45-70 Lee rifles in the United States, including sporting Remington-Lees, although no bolt action became really popular at the time. James Paris Lee's favourite cartridge, at least before smokeless, was the .43 Spanish. It was New Zealand that withdrew 500 rifles amid some acrimony after case separations and breech explosions, although the fault probably lay with the ammunition, assembled by a local contractor from unstamped cases and powder from a manufacturer more used to blasting powder.
There was nothing very original about Lee's bolt, and although the British benefited very greatly from the rear-mounted handle which came after the US Navy Lee, he probably copied that from von Mannlicher. What the British really paid for was the use of the box magazine, although the first use of the double-column magazine was their work. They also dropped his intention to use interchangeable magazines for loading, although this worked out all right when charger loading was introduced.
People do make the .45-70 and the .405 Winchester work in the Lee-Enfield action, although I am not sure if they achieve a totally reliable feed, or with how much trouble. There is a lot to be said, and very little to lose, in choosing one of the .35 or .375 cartridges based on the .303 or .30-40 Krag cases. The .375x2½ Nitro-Express was used in original Lee sporting rifles, sometimes termed the Lee-Speed after the man who developed most of the British improvements, but you would need .405 Winchester cases to make really good brass. This problem doesn't apply with more recent wildcat rounds.
Here are a couple of very good threads on .303 sporting conversions.
http://castboolits.gunloads.com/show...le-(and-friend)
http://castboolits.gunloads.com/show...Sporting-rifle