Do the tuna can test.

Use multiple same size tin cans -- tuna cans, cat food can, or similar.
Set them around the lawn.
Water as usual for 15 minutes.
Turn off the water, measure the depth of water in the cans, figure an average, then multiply the time by whatever it takes to get one inch.

Example with easy math: 1/4 inch in each can. Multiply by 4 to get one inch. Water for one hour.

The practical application:
With some soils, watering for one hour straight means that a lot will run off. So, watch to see what happens. As soon as runoff begins, turn off the system,, wait an hour, then again turn on the system. Repeat until you get one inch.

What Jean001 said. Use any straight sided container to measure water.

You could use a rain gauge if you have one.