what game engine are you planing to go into? BSP comes in many formats. T3D(i think) for the Unreal engine 2.x, .MAP for Quake and a couple of others, .DIF for Torque. All are binary space partition (BSP) formats.
http://www.maple3d.com/GLB2Page.htm allows to generate .map for hl/quake... be aware that the actual .bsp file is the result of a compiling process specific to the engines. so you will need q3map tools or other compiling stuff, that turns the .map to .bsp
Are you sure that Basic is supposed to be able to interpret Max's light objects? You might find that they're used as 'helpers' so the file your exporting is probably okay but the engine isn't picking and interpreting the data properly. Your best bet is going to be to export the models or scene out to ASE and then do a bit…