Sam, you raise a number of good points. You have received numerous good responses. I assume you are talking about being off the grid. Strictly speaking the conventional three phase induction motor is not going to work. As others have pointed out, in a grid connected application, a slightly over synchronous induction motor will push energy into the grid. This is called an asynchronous generator. The field excitation gets to the rotor by transformer action (which is just the relative speed difference between the rotating magnetic field of the stator, driven by the 50Hz grid and the speed of the rotor that is a few percent above synchronous speed - similar concept to how a motor works). Without the grid, there is no easy way to energize the rotor. This is a very simple and robust system, but it is limited to what percentage of the overall grid can be provided (as the percentage increases, the controls get more complicated).
The easy approach is to acquire an electrical machine that allows you to create a rotating magnetic field (preferably in a controllable way - but even that is optional, with enough electronics the energy generated can be fixed after the fact). There are a number of electrical machines that will accomplish this, but they are generally described as a "generator" (or some synonym).
The engine. Yes, you certainly can direct connect the generator. That is a very common approach. As other posters have stated, you simply need to operate the generator at the designed speed - so with a 4 pole generator to get 50Hz, the the generator need to operate at 1500 rpm. That is pretty slow for a Lister ST2. This is still not a big deal, you simply need to derate the horse power expectations (probably quite a bit). There is probably a power curve in the manual, or available on line. Remember that for a 10kW generator, you need nearly 15kW of engine, at the target speed (especially if you are starting a good sized motor). To get enough power, you will likely need to run the engine up around 2200rpm, again, check the power curve. Then you need to ratio down to the correct speed for the generator. Of course the common method is with belts and pullies (certainly numerous other options).
That is only one approach. Since you are off grid, run at your own frequency - how about 65Hz? That will make the engine happier. Then you lathe will simply operate faster than what the name plate says, sort of your own mechanical variable frequency drive (don't try too large a change or the controls will not like it). You could also run all the power through an inverter & frequency drive, but those devices do not like being too far off designed frequency (and you will run into quite a financial cost).
Once you get it sorted, let us know how you worked it out.
Regards, David