On Saturday, August 29, 2020 at 12:20:15 PM UTC+1, ss wrote:
Image below is the cross drive for a mini lathe. It is rusted solid.
I have soaked in WD40 for a couple of days and still stuck.
The arrows in green are points I can tap with hammer but dare not hit
too hard in case the `lug` breaks off.

Never used heat before on rusted items but would `hot air` paint
stripper gun work? I am not too bothered re the paintwork as I will be
repainting the main body before I re assemble the lathe.

Any other ideas?

https://imgur.com/47180QO

It's the temperature/expansion difference that will free it off.
You need the application of strong heat to the circumferential parts.
If the whole thing is warmed, there's no expansion difference so it's less likely to work.
So you want something like a gas torch applied to the bit that needs to be made bigger.