Alwyn,
That is a nasty job to put right. As outlined already, you need to weld the tube, free of the presence of the brass spelter used to braze the tube to the lug. If you have any residual brass in the vicinity, two things will happen. One, you will boil the zinc out of the brass, contaminating the weld and making a hell of a stink. Two, the remaining copper will penetrated the surface of the steel, inter-granular attack I think it is called, embrittling and weakening the steel.
Besides the method already outline, here is another to consider. Cut the frame tube midway between the lug and the front motor mount. Replace the front few inched with a new frame tube. This gets the weld joint well away from the lug, and you have good access all the way around to get a good welding job. But what you say of the bit of frame tube still in the frame lug? Well do not think that you will be able to heat the front lug up and drive it out, this is almost certain to fail. By the time you get it hot enough to free the spelter all the way around, you will have loosened the joint to the front down tube as well. You may find also, that they pinned to joint to hold the alignment while brazing. Probably you will only end up over-heating the joint in an attempt to free it, and boiling the brass as mentioned above.
So I would suggest then boring out the tube. I have been giving this some thought, and I think it could be do with a piloted counter boring tool such as shown:
Larger viewThe pilot would be a free fit in the tube and would guide it two-thirds of the way through the lug. The diameter behind the cutting tool would then provide guidance for the last little bit. Since the fracture is already displaced, I do not think the rest of the lower frame tube can be trusted to provide proper alignment, indeed it may deflect the tool out of alignment when the pilot passes into it. So I think it would be best if the tube were first cut back to midway between the lug and the motor mount, out of the way.
Broken center drills make good boring cutter bits, and it simplifies things by having the cross-hole cylindrical. The alternative would be to broach a square hole to take a small lathe tool bit. A flat and a set screw from the end will hole it in place and keep it oriented. The cutting edge should be about 0.003" proud of the conical step shoulder of the pilot. This is rather important, as it sets the "feed rate" of the pilot. While it may be impossible to feed the pilot too fast, in practice you will be driving this with (I hope) a gear reduced electric pistol drill, preferable variable speed with plenty of torque. So in order to avoid having the pilot race, then bog down and stall, only to free up and race again, it is important to set conditions where the feed rate is more uniform than you may be able to achieve by solely feeding by hand. The rate of cut is determined by many things, but mostly by the relief angles ground on the tip of the tool. These can be hyper critical, small variations determining if the bit does not bite into the metal, or tries to bite too well and dig in. You will have enough trouble adjusting the bit, not to have to worry about that also. So grind the bit to be aggressive so you know it will cut freely, and use the "lead", the 0.003" proud dimension, to limit how much it can dig in. Then you can just lean into it as hard as you can and know it is only going to advance at a steady 0.003" per turn and the speed will be much more uniform.
The other setting of the tool that will be a bit tricky is the tip must bore a hole just a little larger than the shank of the pilot to follow. You can not have a large clearance, as you will rely on the shank for guidance when most of the way through the lug and the lead pilot diameter has been all but machined away. Of course, this resulting diameter should be the size required to leave a gap between the lug and the replacement tube to braze a new joint. I think 0.005" gap or 0.010" on the diameter is about right. Bore a hole in a block of steel the size of the tubing i.d. to try it out and fine tune the pilot cutter. I have not shown and provisions for the swarf. I think flats for such are more likely just to encourage the chips to pack and jam, so it might just be best to pull the pilot out every five turns to brush off the chips and apply some more cutting oil. Flats might work if a second person were available to provide a blast of compressed air to blow the chips through.
I think a butt weld would be sufficiently strong to splice the tube without the need to have a reinforcing sleeve. Due to the torsion bar, there is no room for such inside the tube anyway. You could put one on the outside, but that would be unsightly, and I do not think necessary. If you are worried about the butt weld, then you could cut both ends of the tube at a 45º and scarf the joint, which would be stronger than a joint perpendicular to the axis of the tube. I think the reason it broke the tube where it did is the joint may have been overheated slightly when originally assembled, causing some spelter to penetrate the steel tube. The rest of the joint is backed up by the lug, so no matter if the tube was weakened. But right where the lug ends, it is no longer reinforced. Not only that, there is a stress concentration transitioning from the relatively stiff lug, to the more flexible tubing. So you want to avoid having you weld joint right there, but a few inches away it should be fine. While it is not unknown for Mark frame to break at the front lug, most do not, and it is more common that they break at the rear. My Mark 3 was hit in the front so hard it bent the front down tubes just below the front head stock, and while the frame was cracked in other locations, it did not break at the front lower lugs. So if it just "went", I think some other extenuating circumstances were at play, and not just that the basic design is just too weak. Granted, the Mark frames are a bit flexible, but they usually break at the rear.
Use a piece of aluminum bar turned to be a light drive fit in the i.d. of the tube, to align the ends. Leave this in place to tack the joint, but then drive it out. Use aluminum rather than steel. There is a risk with steel that your tack weld might penetrate through and weld the alignment pin fast. And after all, you do want full penetration of the weld. If this happens with the aluminum, you can at least take a stout rod and drive the aluminum pin back out, even if it means tearing the aluminum past the blobs of weld that penetrated into the i.d. of the tube. If you left the alignment pin in place for the duration of welding, it may be keyed into the weld to such an extent that you might not be able to drive it out. Second, molten aluminum has an affinity for molten steel, the mixing of the two will cause the steel to form a coarse (and weakened) grain structure on solidification. Three or four tacks around the tube will not matter much, but its presence around the entire inner perimeter of the weld is not desired. An alternative, is to use a short length of angle iron as a v-block to align the tubes externally, as related by Eddie above. If the splice is mid-way between the lug and the motor mount, there will be a sufficient length of tube either side of the joint to allow a good alignment.
Then once that is fixed, braze the tube to the lug. Or better yet, use silver-braze (silver solder, hard solder.) Getting the proper free running spelter to wick through the joint may be difficult, but most silver braze alloys excel at this, provided you do leave a gap for capillary action. There are some gap filling silver braze alloys out there, so you can not just use anything to hand. The other advantage to silver-braze is it melts at a much lower temperature (1100-1200ºF) than brass spelter, so boiling off of the zinc (when present) or inter granular penetration of the copper alloying constituents is not a problem. Not that this means immunity, as once you overheat and "burn" the silver-braze flux, you are up the creek without a paddle. The lower temperature will enable you to braze the repair joint without loosening the adjacent joint for the front down tube.
No matter how you go about it, it is a major and difficult repair to do.
-Doug