Nibal,
I agree with Tom. Depending on the size of the lawn, you can use either rotors, rotary, or spray nozzles. Because it is an irregular shaped area, I would go with anything that can be adjustable. I personally like to use rotatory nozzles or spray nozzles just because of the simplicity of the matched precipitation rates and variable arcs. Matched precipitation rates are a bit "tougher" to match on rotors, but it's possible.
Irrigating trees in a turf area, in my opinion, isn't that bad. You ALWAYS want to separate your lawn zones from trees zones. I would design the turf area as usual and have them on their own valves. I would also design my tree irrigation, whether I go with pop-up bubblers, root zone watering bubblers, drip tree rings, etc,. I would have them on their own valves. Program your lawn areas to be watered for as long as it needs to be on for in your climate zone. (Remember that the water from the turf irrigation will also be used to the tree and can act as supplemental watering to the tree and any shallow roots.) Then, program your tree irrigation to run for for slightly less time than normal since the tree will be using the turf water. The tree irrigation will be used to allow to water to penetrate the soil deeper and encourage deeper root growth. Kinda the best of both worlds. Just be sure to not OVERWATER the tree by not taking into account the water from the turf areas.
Hope this helps.