Weird LED light bulb issue
The sockets are wired in series.  For all I know, they always have been. 

You can get away with it with incandescents, at a bit over 1/4 the light from each bulb, so a 150 looks like a 40.     

With one incandescent and one LED, the LED limits current to about 130ma, which is not enough for a 150W incandescent to get up to power.  As such, the incandescent doesn't see much current, and so can't drop much voltage.   Therefore the LED sees near full voltage, and is able to function properly.  

If you want to test the "series" theory, try installing a 150W incandescent in one socket, and a 25W incandescent in the other.  If the 25 is much brighter than the 150, that confirms it.  

Series is not a proper way to wire lights.  The person who wired it doesn't know what they're doing.  Have someone competent fix this and check all their other work.