Single and 3-Phase Load Calculations
It's a 3 x 208V, 200A source (√3 x 208 x 200 = 72kVA) with a phase voltage (line to neutral) of 120V (208/√3).

The total load would be 72kW with 60 lamps rated 120V, 1200W (3 x 20 lamps connected line to neutral) or 60 lamps rated 208V, 1200W (3 x 20 lamps connected line to line).

The total connected load in either case would be 72kW. 

The load could be a mix of 120V and 208V lamps, provided they are equally shared between the phases (balanced load). The load could be unbalanced, provided 24kW per phase is not exceeded (lamps could even be lit between a single line and neutral or between 2 lines). 

The error in your calculations stems from not considering 2 equal currents from each line, with a phase difference between them, when the 208V lamps are connected line to line. Those currents would be (1200 x 20)/208=115.4A. The resultant of those currents would be (115.4*√3)=200A.