Wow there has been a huge influx of 200ES's on here lately... LOL
When you run it out of gas you might have sucked some crap through the carb, i would start with a carb teardown and cleaning, flush and fill the tank, put a new filter inline, that would be a good start.
As for the lights, the headlight and taillight will only work if both the headlight switch and the ignition switch are on, and the fuse under the seat is also good. The indicator lights also run from the power provided by that fuse, so check the fuse.
To check the alternator/stator output that runs the lights and charges the battery unplug the connector with the two yellow wires on the left side by the subtrans shifter and use a voltmeter set to AC or a test light and go across those two yellow wires. You should see voltage there with it running, at idle you should see anywhere from 10-20v depending on engine speed, this is no load voltage so it will be higher. If the voltage is good there then plug it back in and check for voltage at the battery cables to see if the regulator/rectifier is working.
Also you said the battery is dead, remove the battery for now, check the voltage and if its got power while running there then tape off the positive cable end for now until you get a battery. The dead battery could be causing a short so dont leave it connected if its dead/bad.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....