I'm wondering since evaporation is 24/7. Does it really matter when you water? If I water in the heat of the day it may cool my yard down and such the evaporation may be less. Plus since it is a recyclable you can't waste it. So does it really matter when you water? Farmers don't care: they water any time.
Best time of the day is to water in the early morning. The reason is that leaves have the chance to dry before the night, which will prevent mold. For very hot days, you might have to water twice, but usually once a day would be fine (depends also a bit on what plants you have).
I don't exactly understand your reasoning about recycling and therefore not wasting, but in times of drought and when groundwater levels are low, it is certainly advisable not to waste water. A water tank collecting rain water would be ideal for watering the garden.
It's better to water once per week, heavily, than a little bit every day. The roots grow deeper and the grass plants are healthier this way (1 in. per week is optimal for most species, so - one hour of watering during a drought should be all that you need). The Lawn Institute website has tons of best practices, such as this one (Watering Basics).
Grass height also makes a difference in terms of water use (the shorter the height, the more water that is lost). In general, for most species (especially bluegrass), mowing height should be 3 inches. You should also not bag the clippings (they do NOT cause thatch). According to the University of Wisconsin Extension, leaving the clippings on the lawn removes one entire fertilization each year, saving you money and time. More information on mowing practices is here. I encourage you to check out the Education pages on this site - lots of good stuff!
Your question title and your real question seems different.
When it is the optimal time to water? There is just the standard answer: it depends.
It depends on availability of water: on some place you cannot water during the day, because water is used for other important uses. Because pressure and water flow, it is better not to overload water pipes.
Lawn and agriculture are different things. For lawn, you may want to have good roots, to better not to water too often (but see later). Agriculture often have small moveable pipes, so they water 24/7, just different fields on different times. For some crops, it is better to water frequently, but low amount, e.g. to reduce diseases, or just to lower the air temperature, or just not to have irregular growth of fruits.
But it depends a lot of climate and soil. On sandy soil you should not water too much at once, but if is a lot better to have regular watering. On more compact soil, you can water less frequent, but with much more water. In this manner you force root to go deeper, and you will have also less evaporation.
What time? It depends on your location. On valleys, near mountains, near oceans, etc.: maybe morning and evening is not ideal because of wind. When you use the garden? Be sure it is not wet (so possibly not late afternoon, or during daytime on weekends). Do you dislike the sound of watering? So not during night time. Sandy soil? Maybe at late evening (short), etc. So, there is no general rule.
You should adapt to the condition of your garden, your location, and your preferences.