[BroJoeK]

DiogenesLamp to Sherman Logan: "So he was lying to Virginia as well as to the rump confederacy?
If he was going to give up Ft. Sumter to placate Virginia, then how was he going to argue he was "just kidding" about permitting the "rump" to secede?
What presumably was Virginia to gain to induce it to remain in the Union?"

First of all, before the Battle of Fort Sumter, Virginia did vote to remain in the Union, because that's what the majority of Virginians wanted.
What Virginians "gained" was preservation of their political inheritance.

But they remained in convention, threatening to secede if the Federal Government took any actions against secessionists.
What Lincoln wanted was for Virginia's convention to go home so he could take care of business with the Confederacy, and for that, he offered to abandon Fort Sumter.

But Virginia's Fire Eaters didn't want Fort Sumter to end peacefully, since some kind of military battle, any battle, was necessary for them to persuade the majority of Virginians to declare secession.
Lincoln's offer was therefore ignored.

So, please explain, what exactly is your problem comprehending this?

[DiogenesLamp]

What Lincoln wanted was for Virginia's convention to go home so he could take care of business with the Confederacy, and for that, he offered to abandon Fort Sumter.

This explanation plays right into the image of Lincoln the manipulator. You as much as imply that this was just a tactic to gain the upper hand politically, and not a good faith effort to deal with the issue forthrightly.

The salient aspect of this effort is to just get the Virginia convention to go home, and then do whatever he felt was necessary after that political threat had been averted. "Honest Abe" indeed.