Not sure why people want to go to extremes for mounting a small lathe.
A sturdy bench of dimensional lumber like 2" x 4" (4 x 2 in UK and Aus I think) with a piece of 3/4" / 19 mm plywood on top will more than do the job. The 4" dim of the lumber in the top frame should be stood upright for min deflection and max strength. If you face the plywood with a sheet of light galvanised or painted steel you will have easy cleanup and no oil soaking into the wood. For leveling, if you wish to, shims will be fine under the feet of the lathe.
If you have access to an electric welder a bench made of short lengths of angle iron (ex bedframe or similar) and again faced with sheet steel and / or plywood will also work fine.
Extreme materials and weight are NOT required. Slate from the garden may or may not be flat. Don't assume it is.
Just my two cents – your mileage may vary. JD