If the sun is just shining and it's not really hot outside then watering your lawn in the sun is okay and I've done it myself.
Just make sure that when you water the lawn in the sun that the temperature is not above 85 F because the water will evaporate more than it will water the grass and the grass can actually get burned from watering in the hot sun.
So you could do more damage to your lawn watering in the hot sun.
If you need to water your lawn it's best to water the lawn early morning before the sun rises or in the evening as the sun sets or after the sun sets.
I usually water my lawn for 30 minutes in the morning and then once again for 30 minutes when I get home from work.
That gives the lawn enough water and prevents the lawn from getting burnt from the hot sun.