This is a subject that is almost political in nature. Most regard a "Deep and infrequent" plan of watering to be the best approach. The idea is that deep watering promotes deep roots, which in turn enables the lawn to sustain droughts. The evidence supporting this idea is spotty, and the logic doesn't make sense to me. For a full explanation, see my question here
The best counter argument for the deep watering schedule is that much water applied at one time will leach nutrients (calcium, sulfate, magnesium, potassium, nitrates) out of the rootzone, and at the least, cost you more money in lime and fertilzer, and at the worst, harm the grass.
However Los Angeles receives 15 inches of rain per year, which is quite under the 20-30 inches where grass grows best naturally. It also seems water conservation should be a high priority in your area. Therefore, in your particular case, maybe watering more at one time would lead to less evaporative losses than watering at multiple times. Also, your ground shouldn't be subject to much leaching because of the low rainfall (unless you have a fairly sandy soil. A sandy soil will negate everything and require a more frequent watering regardless of evaporation and leaching will be a huge concern). If you have loam soil and little rainfall, maybe it doesn't matter that the lawn is watered deep and infrequently since leaching isn't a big issue and less would be lost through evaporation.
The species of the grass could affect the amount of water required. It stands to reason that faster growing species use more water.
What you really need to determine is the rainfall pattern, the soil type (how much Ca, Mg, K do you have?) and drainage of the soil (is it sandy or clay?) and how much water you have at your disposal. From this you can determine how to keep your soil moist enough, but without any leaching, and without using more water than is necessary.
Then you need to make you mind up on whether you're a member of the "deep and infrequent" camp or the "light and frequent" camp. You also need to decide what time of day is best for watering. Some sites suggest watering at night, claiming less evaporative losses and that the water washes the nutrient rich dew off the plants on which the fungi thrive. Others claim watering at night will surely lead to disease. I feel if a lawn is healthy, it will not be subject to disease. Fungi spores are in the air constantly. The average person inhales 40 spores per day. Only the weak succumb to them. And then, some recommend noon-time watering. Others say the morning is best. Some recommend the evening. Personally, I feel its best to water when the grass is thirsty. Don't make the grass suffer in hopes of building more drought tolerance. I don't believe weakness leads to strength... or that sickness leads to health. If the grass is thirsty, give it a drink. Of course, this would be the time of day evaporative losses would be highest, so it would also be the least efficient use of water. That's a judgement call you're going to have to make. The most efficient use of water would be at night, but that's probably when the grass needs a drink the least.
If you really want to get to the bottom of it, you're going to have to do some research and decide for yourself. Its almost like asking whether it makes more sense to be democrat or republican. There is just no consensus on the matter.
If you want to ask more specific questions, like how much calcium is leached from the ground in relation to other cations? That we can answer.