headlights are wired in paralell, not series. One burned out light should have no effect on the other. Also, since the lights work properly in High Beam mode, it's probably not a ground.
i would use a test light or volt meter to measure current going through the low beam wire at one of the headlights. It's most likely not getting any current.
if no current at the headlight, i'd check for current at the hi/low beam switch. If there is current on the low beam side of the switch, the problem is in the wire between the switch and the headlight....
if there is no current at the low beam side of the switch, the switch is your problem.
I have my money on the switch being bad.......
Quis custodiet ipsos custodes (who will watch the watchmen?)