Lawns are addicted to massive infusions of chemicals and frequent watering. Thes common practices lead the lawn to weakened protection against pests. Shallow grassroots are also prone to droughts. It's rare to find a well-placed organic lawn with healthy soil and deep roots to withstand local conditions, pests, and crowd out weeds.
Pricing on organic lawn care products and services is stip. They are much better for the environment but generally more expensive than regular fertilizers.
If your lawn care is limited to mowing once a week during warm seasons, then going organic will not save you time, but then hardly anything else will do unless you replace the lawn once in a while. You can hire a local lawn care company to take care of your lawn, and install an automatic sprinkler system; it will keep your lawn healthy, but the costs of monthly maintenance will surely burn a hole in your pocket.
If you handle any of these tasks on your own, then organic care may save you some money, but if you live in a drought-prone area, you can avoid water bills.
Choosing an artificial lawn route is aka going organic. You don't need to use chemicals to keep it green and weed-free. No water is needed. There are no "results may differ" sort of situation, and for most people installing synthetic grass is a real lifesaver.