Hi, Not good news ! When the oil supply fails various problems then follow, not necessarily in the same order. The first point of call for incoming oil is the crankcase sealing glands, which in a standard engine is a metal-to-metal seal, so the interface will score and ‘pick up’. The next place for the oil is the main bearings, which soon get damaged if run dry of oil. After the main bearings the oil would get onto the rear face of the cranks, and by centrifugal force it gets thrown outwards into the groove on the edge of the cranks, and from there into the big-end bearings, so they also suffer if the oil supply fails. The cylinder walls get their lubrication by means of the petrol vapour passing through the crankcase picking up some of the oil that has been lost out of the big-ends, which collects in the ‘wells’ at the bottom of each crank chamber. Once that has been used up, the piston rings and bores will run dry of oil, then overheat, causing the pistons to expand more than usual, to the point of seizure. Usually the piston metal will melt in small areas, and be ‘wiped’ onto the bores.
Perhaps your best initial action will be to take out the spark plugs and squirt some penetrating oil into the bores. You could also take off the transfer port covers and see if this reveals any damage. After standing for about 24 hours, put the bike in top gear, then rock the bike backwards and forwards to see if it frees off. Even if it does free off you shouldn’t run the engine again until both it, AND THE PILGRIM PUMP, have been stripped for inspection and repairs.