My desk is a classic McDowell & Craig tanker, famous for being built like a battleship. All its drawers secure when shut and are conveniently released by opening the pencil drawer in the middle which has the only keyed lock--a wonderful idea until the mechanism starts sticking as it is doing right now! Panic time as I have important things in there! What step do I take to open the drawers on the right when pulling the drawer in the middle doesn't release them as normal? Is this a lubrication gremlin?

Most likely when you close the center drawer that moves some mechanism that physically prevent opening the other drawers. Since you are having problems with the right and do not indicate problems with the left, there are two devices, one for the left and one for the right. Probably rods or bars that are moved when the center drawer is closed.
If you open the center drawer and look underneath you will see the mechanism and how it works. If you remove the drawers on the side you should see the device that actually prevents the drawers from opening. Probably a rod or bar that moves up and down or to the side.
I doubt that what is needed is lubrication per se. More likely adjustment, wear and tear or something interfering with its operation (that bundle of money you are hiding). This will be a mechanical operation, (one leaver pushes another). Its operation should be obvious when you see it.