I picked up a really old small no name lathe. Didn't need it, but it was too cheap to "turn down." The tail does not turn, so its age is pretty old. I don't know whether to cut it down and take it with me when I camp or not. I thought about loaning it to a local museum in the small town down the road. What is your suggestions?

See if the museum is interested, if not it can be whatever you want it to be.  Spindle turning may be all it is good for.  Older lathes didn't lend themselves well to the new chucks and other equipment available these days.  Pictures would help to make a more informed suggestion.

Hmmm a lathe?  Well if you can get a chuck in it (if it's got a taper then you can)  then it can be used with a  large brad point bit and a table to start DTs by roughing out the waste.  I worked at a hand built furniture place in Boston where they had some really ancient shop built tools including a stroke sander, all shop built, that could take a 20' piece. There was a selection of  shaped sanding pads for doing molding.  But I digress.

The DT machine had a horizontally mounted chuck with a brad point bit in it and a table that ride on ways in and out of the bit but not laterally.  You'd mark your drawer side,  put it  on  the table against the wood fence  and shove it in, hit the depth stop and repeat for each of the pins or tails wasting the wood out.   Then just finish with a chisel.  Worked on mitered hidden tails too.

 

I converted  an old crapsman tube lathe headstock  into a variable speed  10"  dual station grinder station

 

Hoirizontal boring for dowels comes to mind.

 

 

 

Donate it to some young kid that would love to have it...