This lawn is almost too steep to not have any terracing, leveling and retaining walls. If not done correctly, with heavy watering or heavy storms, most of the water will roll off the hill before it has time to soak in. See watering lawns on slopes and hillsides for more ideas about this.
The two planting areas where the trees are are in need of some leveling in order for proper saturation depth to the root zones. It's a great opportunity to add a little class with some retaining wall ideas while giving the trees a better chance of survival. Simply leveling the hillside slope and adding some simple concrete block retaining walls would be an easy and inexpensive do it yourself project.