Did I accidentally wander into a woodworking forum by mistake!?😲😄
Wood!? It takes on moisture, moves, and makes aluminium look like granite, where stability under temperature and humidity changes is concerned!
If at all possible, the stand for a lathe should be made out of steel.
I made a perfectly respectable stand for my Warco Minor mill out of box section with a cheap Parkside (Lidl) flux core welder. I had very little welding expertise (I had never touched a welder before I bought the Parkside welder) and as ham-fisted as I am, the stand is very solid.
Now, I went a bit mad and used 50 mm box section with a wall thickness of 3mm. I am not particularly looking forward to when the time comes to move the damn thing (and it shouldn’t be that long since the Warco mill has to be sold due to me getting the AEW Viceroy mill).
I reckon 40 mm, 2 mm wall thickness box section should be fine. It’s not expensive, you can buy it from sellers on eBay pretty cheaply. Keep an eye out for cheap flux core welders on eBay, and for the return of the Parkside flux core welder at Lidl (it shows up a couple of times a year), it was £80 IIRC.
Teach yourself to weld, it’s really not hard to do (especially flux core welding) and you’ll have a very useful skill that will be transferable to repairs outside your shed too (although I’d caution against repairing anything that someone’s safety, health or livelihood depends on; don’t offer to fix your neighbours car for instance! 😄).