The answer is Morning. Get going as the sun comes up. Water the lawn in the evening when it is a little cooler. If you water when the sun is shining, most of the water will evaporate in the heat.
So why shouldn’t you water at night time? Because your lawn can stands a better chance of getting diseases like mold if you water at night. Mother Nature may choose to do this occasionally, but you can control it. Allow enough time for your grass to dry before nightfall.
In other words, water thoroughly but seldom. If you have a newly sown lawn, it is important to water little but often.

Most homeowners water their lawns too much rather than too little. For the health of your lawn, and to conserve water, you want to try to provide the amount of water that your grass needs to thrive? No more, no less.
In a normal summer you should water at the end of May, July and August. But you have to water thoroughly- approximately 20-30mm-in order to achieve a good result. If you water too little, the water will not find its way down to the deepest roots. They will consequently try to grow upwards towards the moisture, and the result of your efforts is most likely to be negative for the grass.
Grass needs about one inch of water per week. How do you know how much water you are providing? The only precise way is to measure it. You can buy a rain gauge or make a simple one from a tuna can. Mark one inch in depth on the empty can, then place it in your yard where you are going to water.
Water your lawn for 20 minutes and see how much water has accumulated in the can. This will help you adjust your watering knowing that a good general goal is one inch of water per week. This one inch may be best applied in two or more waterings rather than one ? it will depend upon your soil type. With a sandy or light soil, the water will run through it more quickly rather than hold it. For this type of soil, light, more frequent waterings will be more beneficial to your lawn.