I’ve got an old Craftsman 103 lathe from the 1940s or so.  I’ve had it for a while, but have never really got it into working condition.  The motor works, and everything seems pretty much fine with it, except I need to make a sturdier bench than the one I built out of scrap wood and rusty nails years ago.  It’s just not sturdy enough.  It will jiggle around if you lean on it.

My main concern though is that when I look at the pronged driver on the headstock it seems to have a lot of runout.  I move the spindle by hand, and I can see the center point of the pronged drive wobble.  I don’t have a dial indicator, but I would guess that it wobbles by somewhere around a 32nd of an inch or maybe even a 16th of an inch from one side to the other.  I pulled the pronged drive thing (I don’t know what it’s called) out of the morse taper hole in the spindle, and it looked like the morse taper hole in the spindle is actually off center.  I swiveled the tool rest over so it was just touching the lower edge of the morse taper hole, and rotated the spindle by hand.   I’m not sure how to measure it, but I can see the morse taper hole moving in relation to the tool rest.  It’s definitely off center in the spindle.  Maybe by a 32nd.
I guess my question is how perfectly centered does a lathe have to be to do basic work?  I don’t want to buy a new lathe.  I looked for a supplier of spindles for the 103, but Sears doesn’t carry the part any more, and there’s nothing on E-Bay. 

If this thing is off by a 32nd, can I still use it with success?