Replaced all the antique devices on a control cabinet door with Allen Bradley 800B devices. All work fine but those on a heater control circuit. Cycling the heaters a couple times kills the 800-N5R lamp (which is an LED on 120volts). Without an oscilloscope, I'm guessing a spike from the heater coil. Maybe low circuit impedance? I'm just a dumb ole electrician and don't know how to size the resistor or diode needed. Any help?
You need to investigate it a little further first, this could be one of two things (maybe more). It's fairly uncommon for LED lamps to burn out like that.
It's possibly because your heater has a high PTC of resistance (Positive Temperature Coefficient) which means when it's cold the resistance is low and as it heats up, the resistance increases. With that type of heater element, there is a big spike of current when you first turn them on, which can cause a severe voltage drop. In that case, a resistor in the pilot light would make it worse, a diode would do nothing (and by the way, an LED already IS a diode). For that, you might want to look into a solid state relay to ramp the voltage into that heater, because it's not just the lamp that's going to give you fits, sooner or later.
The other possibility is that your heater is fed by a transformer, and you are getting inductive kickback from that transformer winding when you turn it off, which becomes a severe voltage spike. The best thing to do on that is to suppress it at the transformer because it too is causing you problems elsewhere that you might not be seeing yet. You can go buy a RC Snubber for the pilot light, but if you do, buy one for everything else on that circuit too.
Think of that pilot light as being a canary in a coal mine. Buying a gas mask for the canary does not solve the real problem!