You certainly do notshouldn't need a pump with that much head. Here's the secret to getting enough waterflow to sprinklers. You don't need to run them all at the same time.
So if you have 4 sprinklers and only have the flow to run 2 of them happily, then simply have 2 zones. Run one until it's done. Then run the other.
Best to do it at night - you'll lose less water to evaporation.
Another trick you can do is reduce (ratchet back) the run-time of the sprinklers. Lots of people vastly, vastly over-water their lawns. Reduce the runtime by 15% a week until the lawn starts to show distress... then increase it back up one notch.