ignition off, lights stay on

Where did you connect the coil of the relay to?  Is the voltage on the coil dropping out as soon as your turn the key off?

It sounds, to me, like maybe you connected to a RAP wire instead of a true ignition wire.

Thanks for the replies.  Howie ...would you expand on that a little, please

K Pierson...I have been wondering that myself.  I'm not familiar with a RAP wire, can you explain.  We DIYers think we know everything but obviously, we don't.  I believe the wire that I tapped for the coil is the oil pressure circuit.  I'll have to do a little mor research on that.

OK, the diodes isolate your circuit and prevent coil on-rush back EMF.

Try finding a proper ignition wire that shuts down on turning off the ignition OR if there's a second ignition wire at the ignition switch that gives you 12v+ on ignition but dumps when you turn the key to the starter.

RAP = Retained acc power, I'm not even going there until you tell us what vehicle this is. Wiring pathway should be 12v+IGN 2 to 86, ground to 85, 12v+ constant at 15amps fused to 30 and 87 to foglamps. You shouldn't need any diodes that way because the relay isolates your feed from the regular fog light circuitry. N.B. An oil pressure feed isn't at a constant voltage, it's going to go from ground to about 3volts ref. Although KP might correct me on that. It certainly won't be 12volts, also on a modern vehicle you might upset the diagnostics/engine management tapping in at that point.