You don't need to run a neutral if the load doesn't need a neutral. 208V lights just need the two 'hots'; there is nothing to connect the neutral to. If you also have some other loads (such as control devices) that require the neutral, then run the neutral.
With lights spaced out as you suggest, an easy approximation is to treat the full load at the average distance; so take iwire's current number of 15.4A but at 575 feet rather than 1000 feet.
You start with the 208V. Now you multiply by the allowable voltage drop. Iwire used 3%, and that is a reasonable number, but you really need to make a design decision based upon the lights that you are using. If you can tolerate a 5% drop, then you can use smaller wire. Working with 3%: 208 * 0.03 = 6.24V
The allowed 6.24V is on two conductors together, so you only get 3.12V of allowed drop per conductor.
You take the allowed voltage drop and divide by current to get allowed resistance:
3.12 / 15.4 = 0.2 ohms.
From the allowed resistance you can calculate wire size. This is easy to do with tables. The tables normally list 'ohms per 1000 feet' or something similar.
The above calculation gives 0.2 ohms per 575 feet, or 0.2 / 575 * 1000 = 0.35 ohms per 1000 feet. Now you go to your table. The result is somewhere between a #5 and a #6 copper conductor; you can't buy #5 and #6 is slightly too small (given the above assumptions). If you accept a 3.5% drop then #6 works.
Note that the difference between the #3 that iwire suggested and the #6 that I mention is because of a change in assumptions going into the calculations. Iwire was calculating with the full load at 1000 feet, I was calculating with the load at an average of 575 feet.
Changing assumptions again: if you can run this as a 3 phase circuit, with 3 hots and the lights balanced between the 3 legs, then your current per leg goes down, and you can work with #8 conductors.
This is why the missing details are so key; just by picking different design parameters, the solution is anything from #3 conductors to #8 conductors.
-Jon