Michael,
This is the method I have used to repair similar breakages. Firstly, clean back to bare metal the area around the break. Carefully trim back the lug until you have at least 5-6mm of tube clear of the lug. Very carefully, clean up the tube so that there is no sign of the brazing on the exposed tube (any braze will contaminate the subsequent welding, leaving a brittle joint). 'V' out the joint by just over half the tube thickness, and if possible, fit a thin sleeve inside the tube (to keep the ends lined up). Get a welder to 'Argon Arc' the ends together again. After fettling the joint, build up the lug again to it's original shape (either with silicon bronze weld, or body filler (just for cosmetic purposes)).
Having made the repair, make sure it is not going to re-occur - a contributing factor to these cracks is often poor lubrication of the swinging arm pivots. You will find that, if still fitted with the original pivot pins, they are drilled right through - resulting in the use of the grease gun pushing the sealing plug out of the end of the swinging arm lug (rather than pushing grease into the bearing). If the sealing plug is already out, press a tight fitting plug into the end of the pivot pin, then fit a new sealing plug. If you need to push a sealing plug out, remove the retaining plug/grease nipple from the outside of the pivot, and use a drift to push the plug out.
I hope this all makes sense,
Regards,
Eddie.