2 wire? No ground?
Does it have a nameplate that you can post a Pic of?
Once started up, it should run on a 1kw, but the startup current will be a lot higher. My guess is you'd need a 3kw and even then, it might trip the generator if it can't react fast enough.
I had a 1/2hp pump that would run fine on my 5.5kw inverter generator and a 7kw regular generator, but I never tried it on less.
One issue you will have is the 240v as small generators are almost always 120v.