Here is what I know.. And you can take it for what it's worth. I too love taking care of my lawn.
Bear in mind, all of my research is north central region of the United States. So it could potentially be very different where you are.
First and foremost, giving your lawn the full amount of water. It was recommended in most places to make sure you give at least an inch of water to your lawn. This helps the roots grow much deeper. I use a Tuna can when I use the sprinkler. Once the Tuna Can fills up, I feel satisfied that I have given it enough water.
Part of watering in the morning versus the night is basically to promote a healthy growing cycle. Imagine if you drank 10 glasses of an energy drink at midnight. Assuming your not a night owl, we can say that you're not getting any value of the 10 glasses of energy drink. So, it just sits in your system, disappears.
Now drink those same 10 glasses in the morning when the sun is shining and all is well to begin your activity.
Grass is not much different. It has a period of the day (Namely when there's no sun) where it does not continue to drink water.
So watering in the morning is the perfect time because grass is starting to utilize that water.
Now, it was said to me that watering at night is better than not watering at all. The side effects are that you tend to lose some of the water as a waste. It is evaporated into the soil and the grass never utilized it. Worse yet, the water can actually produce a mold because it sits stagnant without getting used.
Watering in the mid morning, afternoon isn't all bad, however as I understand it, the problem there is that there is a chance that dew beads on grass from the water actually create a magnifying effect and can burn grass. I think worse than that is the chance that it evaporates because of the hot sun, so you're not getting you moneys worth.
As I said before, I am no expert by any means. A friend of mine is an owner of a local Irragation (Sprinkler System) installation business. He claims that he sets up 95% of his systems to water between 4:00am and 6:00am.
Hope this helps...