Lawns should be watered between the hours of 2am and 9am (or thereabouts). Evaporative loss is a concern for two reasons: it's a waste of water, and when a significant proportion of the water you apply evaporates, your turf isn't receiving as much water as you think it is. But even if you account for this evaporative loss (and you should) and don't care about wasting water (you should care), it is still important to limit your watering at a time that doesn't extend the amount of time your turf is wet (from dew, for example). If you water at 8pm, you are extending that wet time by 6 hours or more. Diseases, especially fungal infections love wet turf, and the longer the grass is wet, the greater the chance of infection. By 4am, your turf is already wet with dew, and it will dry out once the sun comes out again.
Just as important as the question of when to water is how much and how frequently to water. Water as infrequently as possible while still providing the proper amount (here is a nice guide, though every state will have one: http://pubs.ext.vt.edu/430/430-010/430-010.html). A typical lawn needs (depending on soil, location, grass type, slope, etc.) between .75" - 1.5" of water a week (including rainfall). The only way to know how long to water is to know how much water your sprinkler applies in a given time (see How to Calibrate Sprinkler Heads - http://edis.ifas.ufl.edu/pdffiles/LH/LH02600.pdf). Only after you know this can you determine how long you need to let those run.