For the lawn, frequent short irrigations are fine, but for a tree this irrigation frequency favors development of a shallow root system. By supplementing the short frequent irrigations with a deep irrigation specifically for the tree, you will encourage the deeper root establishment.
Mowers or string trimmers wreak havoc on trunks of trees planted in turf. Some types of trees are more sensitive to this damage than others. However, the health and vigor of most tree species can be damaged by even moderate trunk injuries, which are inflicted at least twice a month in most landscape situations. Even slight injuries to the trunks of some trees can cause loss of vigor. Trees like blue or Sonoran palo verdes and many other desert trees have a very thin layer of bark protecting the conducting vessels that lie just under the surface.
Beneath the bark are vessels that carry sugars produced in the leaves to the roots; another set of vessels carry nutrients and water taken up by the roots flow to the above ground tissues. The sugars, water and nutrients must pass through these vessels in the trunk. In trees that have a thin bark and a soft trunk, even a relatively shallow scrape can disrupt the flow of sugars, water and nutrients. There must be enough intact vessels left to transport enough sugars for the roots or enough water and nutrients for above ground tissues. If not, branches and roots can dieback or the tree can be killed.
A turf-free area surrounded by physical barriers, guards or trees wells around the base of the tree can force lawn equipment to stay at a distance. Planting shrubs at the base of trees will also keep implements away, but put in plants that have water and nutrient needs similar to those of the tree. A circular concrete or brick boarder will keep lawn mowers away. A loose ring of chicken wire around the trunk can also prevent damage, but it must be loosened as the trunk grows. If the chicken wire is tightly wrapped around the trunk, the trunk will be cut into as it grows and the conducting vessels will be damaged. Herbicides can be used to burn back weeds that grow near the trunk. Avoid getting herbicides like glyphosate (Roundup) on the leaves of the trees. Roundup and similar herbicides are taken up by the leaves and is transported to the roots. It will not damage the tree if there is contact with the bark.
There are a few things you can do that will lessen the chances that you will have a problem with your trees or lawn. Occasional long irrigations around trees will provide the tree with the water it needs deep in the soil and will not damage the lawn. Thin out branches of trees where branch growth is very dense. Some type of protective barrier should be placed around the tree to prevent lawn equipment from damaging the trunk.