This lathe is missing the casting and microswitch assembly that supports the leadscrew and feed rod. This would be substantial work to remake, but not impossible. Carriage handwheel is also broken or missing, as is the collet closer (it used to have a lever collet closer).
My guess is a very devoted party could salvage this, but it would be lots of work. Spindle bearings could be rusty which would stink to replace, but they're probably fine given how protected they are. Might need a new leadscrew, but this can be made from 1144 or the like; the original Rivett leadscrew isn't hardened (mine cut fine with HSS). Cleaning up the tailstock might require chroming and regrinding the ram. Way can probably be cleaned w/ steel wool and used as-is. Apron is aluminum, so that's fine, but might need a new apron oil pump if water has collected (not super difficult to make on a bridgeport). QC gearbox is a modular unit; it's probably good as new.
If I wanted a project, this is priced right and the results would be a nice machine. But it's rare to find folks with both the skills and time for this. I'm not sure I have either. I wish I had this when I was in highschool; would've been a much better project than the SB heavy ten I "rebuilt".
I enlarged the pic and I am sure it has a long taper locking ring next to the chuck. It could be L0 or L1.
Rivett 1020S & 1030 Lathes
Larry
Looks the same as the L0 spindle on my 1030F. That said, the locking nuts on them are large; I appreciate that Rivett didn't skimp on the spindle taper for these.
P.S. Blaming a rusty lathe on "environmentalists" is pretty funny. Thanks for the chuckle Trev.