Presuming that we talking about flourescent or discharge lighting with electronic ballasts, then 277 volt operation is very slightly more efficient.
All such ballasts use DC internally, with the incoming supply being rectified.
The losses in the rectifier are the product of a fixed voltage, about 1.6 volts, and the line current, which is less at 277 volts.
Consider a ballast with a current draw of 1 amp at 120 volts and a voltage drop in the rectifier of 1.6 volts, this is clearly a loss of 1.6 watts.
Now connect the same ballast to a 277 volt supply, and it will draw about 0.4 amp, the voltage drop in the rectifier is still 1.6 volts, giving a watts loss of about 0.64 of a watt, and saving about one watt.
Therefore there is a saving but it is very small.
The watts input to a ballast is normally only stated to the nearest whole watt, therefore on small ballasts the tiny saving is hidden.
For example a ballast that uses 29.8 watts on 277 volts, and 30.1 watts on 120 volts, would be described as "30 watts" on either voltage.
If the building has 277/480 volt service with 120 volts being obtained from a transformer, then working lighting at 277 volts will avoid the losses of a few % in the transformer in addition.
On a new install, the transformer would be smaller and therefore cheaper in addition.
However as others post, the biggest saving is on time and material.
Many more lamps can be installed on a 277 volt circuit, compared to a 120 volt circuit.
In many cases a smaller wire size can be used.
Code requires a minimum of #12 on a 20 amp circuit, however in practice on a 120 volt lighting circuit, #10 or even #8 may be required in order to avoid excessive voltage drop. (unless the circuit is very short)
At 277 volts, the minimum wire size permitted by code will often suffice.
Although the NEC does not place any exact limit on voltage drop, 3% is often regarded as acceptable.
3% of 120 volt is of course 3.6 volts.
3% of 277 volts is about 8.3 volts.
Therefore a 277 volt 20 amp circuit can be well over twice as long as a 120 volt 20 amp circuit, before voltage drop requires larger conductors.