The BAR wasn't a light machine gun, it was an auto-rifle (hence browning automatic rifle)
The Lewis gun was reliable, but heavy and had some trouble jamming due to its drum clip. Still it was probably the best for bite-and-hold operations, where the infantry were expected to take an objective and were forced to hold out until reinforcements and regular machine guns arrived.
The Chauchat was pretty bad, but if you found one that worked, it was the best weapon available. Even the German Flammenwerfer units, a special operations force, paid its men to collect the Chauchat, which armorer personnel would then modify/improve behind the lines, often combining parts from units to create reliable weapons.
When it worked it was light weight, high rate of fire, reasonably reliable, and powerful. Also it could be fired on the move, which neither the Lewis gun nor the Mg08/15 could. That made it great for quick moving assaults, which light machine guns were really supposed to shine.
So I'd say that the Chauchat was the best when it worked, but otherwise the Lewis gun was more reliable despite all of its drawbacks.