Two 10″ inline filter sumps will take care of any sediment problems that you have. Use a 30-micron filter first and a 10-micron filter in the post position. Check them every month until you can forecast the replacement.
Try turning up the pressure switch looks like a small gray box wired to the motor located near the pressure tank. As far as pressure for watering your lawn the added filters will further reduce the pressure available up to around 15 PSI. Check the rated output of your pump against what is actually coming out of it.
If this is no help you may want to reconsider the type and make of the pump used, if a lawn was not considered for it’s original design then its time for an upgrade.
You may want to add a break tank to pool the water for your lawn add a second boost pump to be used only when the sprinklers are being run.
David F. Walling