Lawn irrigation system with shallow well supplied water is slow to start spraying at sprinklers
The type of system you have makes a difference. In my area jet pumps are quite common and they do deprime from time to time when the foot gets stuck open. They also can have issues with the jet assembly or the pump. How do you know if you have a jet? There will be 2 pipes going down the well with the motor at ground level or in a pump house.
A submersible pump usually doesn't deprime because the pump is below the water level but many times they do have a check valve up top.
A self priming shallow well pump is another type but these sometime do need water in the pump if the water level is low and they usually do have a foot valve. As these pumps age and do not produce enough vacuum or if the water level falls below its lift value they quit working.
I would be pulling the lines down the well shaft as jets are usually 50’ or less in my area and single pipe shallow well are around 20’ so both are usually easy to pull up and check the foot &amp; or jet. If those are good the pump could be worn out.