On Tuesday, August 8, 2017 at 7:30:07 PM UTC-5, bob prohaska wrote:

It's not obvious to me how to disassemble it for repair, nor what adhesives
to use.

The top should separate from the pedestals'assembly fairly easily. If there's not any fasteners readily visible on the exterior, then they are inside the carcass, inside the drawers. Probably metal fasteners, like "L" brackets.

Once the top is off, the two pedestals are held together by a spanning element (panel), between the two. Again, there is likely metal fasteners holding the spanning element to each pedestal.

If there is no visible fasteners, look closely for a screw site. The screw may be recessed, with a plug hiding the screw head. The spanning panel would likely have to be fairly thick, to have recessed screws, that way.

I think you would need to remove the top and probably the spanning panel, before you can properly access the damaged leg(s). I would think there is more than one M&T joint along each leg and, if one is disjointed, then the other has likely been compromised, as well.

The general design of almost every double pedestal desk is very similar. Rather than google Lincoln pedestal desk, try oak roll top desk. I highly suspect your desk is assembled, basically, the same way, in some similar fashion.
https://www.youtube.com/watch?v=_VpXtbgHXMg

Once your basic assembly is disassembled, then you can address the assembly (repair) of any individual part. If your desk is assembled differently, in some unique way, then maybe you have some special piece of furniture.

Yep, pics would definitely help.

Sonny