Mogrix,
Please post this picture on the Lawns forum
Not to say that some people here won't know the answer
for you, but there are pros on the lawn forums who will give you an accurate answer quickly.

The picture is not very clear but since I have had the same effect, I can suggest a relationship. I have had dried out lawn area that is above the septic leach field. The fields are either linear trenches or one trench that snakes back and forth.

Admittedly, this seems counter intuitive considering the phrase 'the grass is always greener over the septic line." I have one theory created out of thin air. Until this year I have had a lot of Japanese Beetles and I know that the grubs like to eat and kill turf grass. Perhaps they are attracted to the damper regions and kill those sections. I have not had the streaks this year, but until last month, the lawn was well watered from consistent rains.

The leach field comment would make perfect sense if in fact the fields are linear parallel trenches. reason being is that there is a layer of crushed stone then dirt on top basically causing the soil in the field to drain faster and dry out faster. whereas the rest of the lawn is just deep dirt that retains moisture, this section will be the first to dry out in the summer. hope it make sense. if you google leach field diagram you will have a better idea