Right, well Im in East Yorkshire (Driffield) so I can't "pop over for ten minutes" Now we know the starter and motor have worked together before, and the starter is a much smaller ones than I have ever worked on, I would have a clean at the top, and see what it says, apart from "made in England" and also the plate at the front, to see if it says DOL (direct on line). As there are only three wires coming from it, we can assume it is, and connect the three wires to the three wires from the motor, the worst it can do is go the wrong way, so make sure the machine is out of gear. If there are any switches or stop buttons on the lathe, you ought to take the tops off and check the condition of the wiring, as these starters came from an era when the wiring was usually VIR (vulcanised india rubber) which is a matt reddybrown colour and is covered with a woven cotton outer sheath. This cable is usually in perfect condition where it is inside a conduit, but tends to dry out at the terminations, with the result that all the insulation falls off! Also it does not like oil, which makes it go all sticky and it can catch fire! If it is VIR I would rewire it in pvc singles to be on the safe side, then megger the whole machine, not just the motor, as vir itself can be "leaky" electrically. With the POWER OFF!! and with the tank off. move the handle on the starter and see if it just moves one position from off to on, check the movement underneath, and check for loose contacts, or anything that looks burnt. The good news is that you can take a fine file to the contacts and restore them to as near to the original shape as possible. WITH THE POWER OFF!!!!! operate the handle and check that all the contacts meet with reasonable pressure as the handle gets to the run position. Filter the oil through the wifes best tights, clean the debris out of the bottom of the tank, refill and give it a try! Some Ellisons have mechanical hold in when in the run position, some have electrical hold in using a coil. With mechanical hold in, the overloads will mechanically trip the stop mechanism, with the electrical system the overloads drop the coil out and the starter switches off, mechanical ones do NOT release on no volts, so beware if you have a power cut, as the starter will stay in the on position and the machine will restart when power is restored!! TBH I am pulling all this from memory, and it is a long time ago, so if you can get a knowledgable "old" sparky on the job, do it! Anyone trained later than the early eighties will run away screaming when they see this equipment!
Phil