Is that lifted veneer? or just damaged finish?

Agree with Al... if there is a void between the veneer & the substrate, it's going to have movement, suggestion it can be glued & pressed/clamped back down. But if the substrate has swelled up, causing the veneer to raise, it will be more of a problem.

I cannot determine if it is separated from the substrate. Seems very solid. I wonder of the substrate just swelled?

From the edge where the leaf is, see if you can slip something very thin, (putty knife) under the veneer. If so take a peek and see if you can tell if the substrate is swollen. If it is MDF and has gotten wet and coming apart, this is not a DIY job.

Push on the discolored part....you should be able to feel it give just a touch if it has delaminated.

Not all delaminations "give". I've repaired many that were tight against the substrate, but not glued.

As far as refinishing the water damage goes, if the finish is original, it is most likely lacquer, given that it dates from 1961. Get some lacquer thinner and 0000 steel wool. Put a little thinner on the wool and rub it over the damaged bits. It might dissolve and redistribute it enough that you won't have to do a full refinish on the top. It might take some elbow grease. Be careful not too use too much thinner or it will carry away the finish.

I had some time to look at this.

I now think the top is particle board center with solid wood on the edges.

So the particle board has swelled. Still looks like the laminate is tight to it.

I tried denatured alcohol - it did nothing

I tried lacquer thinner and softened and started to remove the finish.

The odd thing is when I rubbed the lacquer on the edge where the solid wood is. It took the color off also?

No surprising that alcohol didn't do anything. Also not surprising that the lacquer thinner took off the color also. It's a factory made product and many factories mix stain and finish together to save time in production.

Since the particle board has swelled, the correct way to repair it is to loosen the veneer to a point where it can be peeled back and the swelled particle board can be sanded flat. Do not try to sand it flat without removing the veneer, you will sand through the veneer. Then the MDF needs to be reglued, by letting some kind of adhesive soak in and harden. I've used super glue or epoxy (with a heat gun) to re-solidify the MDF. Then smoothed again and the veneer glued down.

This is not a task for the inexperienced. If the table means something to you, take it to a pro.

Heat gun may loosen up the glue so a putty knife can peel up the veneer.

To totally remove veneer I wet a towel and wring it out. Spread it over the veneer and let it sit overnight. The veneer usually lifts right off. Mind this is not for when you wish to save the veneer. Lifted edges I take one of my syringes (I have horses and save and rinse out ones from vaccines for projects). Suck up some wood glue and inject it under the lifted area. This is also great for loose rungs on chairs or filling small cracks. If rinsed well one syringe can last years.