The voltage is OK, it is/was quite normal to under-run incandescent lamps when full brightness isn't needed. It greatly extends their life which is of course important when the lamp isn't easily replaceable. I'm not sure how you took the current measurment though. You would normally use an AC current range and on a lamp with those ratings I would expect the current to be around 150mA but if it's burned out the current would be zero. You can't just put a current meter across the lamp connections because the lamp itself has to limit the current, without it in series you run the risk of damaging your test meter.
Anyway, yes, that LED or just about any other "hi brightness" one will work, I suggest you add a diode in series with it, even a small signal diode like a 1N4148 will work and also add a resistor in series with them. So you have the three components in a chain across the original lamp connections. The resistor should be 180 Ohms.
The data sheet doesn't say which pin pf the LED is which but usually the cathode side has the small flat section of the body beside it. The LED and the normal diode should be facing the same way so the banded end of the diode goes to the side of the LED WITHOUT the flat on it. If in doubt, wire it up and connect it across a 9V DC battery, if you have it right, it will light up when the battery is one way around but not light when it's reversed. Because the lamp runs on AC, it doesn't matter which way round the connections to the lamp holder are made.
Brian.