Any engine can lose oil in three ways - leaks, worn pistons/rings, worn valves/guides.
Leaks Front/Rear Crankshaft Oil Seal - These require an ungrooved, rust free ground finish to run on.
Front Sealing Block/Rear Oil Seal Housing - As these are made from aluminium they are very prone to stripped threads.
Head Gasket - In the left hand rear corner, there is an oil feed to the rocker shaft. Use HYLOMAR round the hole for the rocker shaft oil feed. Pushrod Guide Tubes - (when fitted). You Tell Me!!!
Worn Pistons/Rings The only real cure for this is a rebore and new pistons, because if the pistons are removed from the bores, the block will need honing and new rings fitted. Worn Valves/Guides For some inexplicable reason, Triumph did not fit valve stem oil seals, relying instead on a very close tolerance between valve and guide to prevent excess oil loss. We have recently found valve stem oil seals that can be fitted to a range of our engines and have found them to be extremely effective in controlling the flow of oil down the valve stem (see pt no. HR631 Note this is not suitable for all engines). Remember these are only needed on the inlet valves, and they won't fit with double valve springs.