@tundrawolf
To be clear, the guys are concerned that you may damage your lathe by welding things held in it.
How?
1) if you put your ground lead on the lathe base and you weld two parts held in the headstock and tail stock chucks, then all that welding current thru the ground lead MUST go thru the spindle bearings, chuck jaws, some thru the ways to tailstock interface, etc. You could seriously damage the headstock bearing or do a little accidental welding on one of those interfaces.
2) Even if the ground lead is connected directly to the work-piece, the inevitable weld spatter on the ways can wreck them
Can you instead use the lathe to turn a mandrel that both tubes can be slid onto to align them and then weld the two tubes together while on the mandrel? (far away from the lathe). Even if the two tubes have different inner diameters, you could turn a mandrel with a step/shoulder to account for this.
As for the welding, I think you are correct about trying to balance the heat in an attempt to minimize warping. Start with one tack weld, then quickly do another 180 degrees away, then a pair 90 degrees to the first two.
What welding processes do you have access to?
-brino