Believe it or not, this is a rather difficult question to answer, and there’s even a lot of debate amongst the professional community. It’s all dependent on your species of tree, site characteristics, and how you have maintained it in the past. Trees that receive a lot of water because of grass will always need a lot of water. That’s because the tree has changed its anatomy to compensate for the change in its environment. Believe it or not, most trees here in Utah are overwatered, but because of the prolonged drought we have experienced, those overwatered trees are now in massive drought stress. To answer your questions in short…enough to keep it alive, but not too much to drown it. If your grass is nice and green, long and thick… your tree is getting overwatered. For more information on how to treat a drought-stressed tree, please see link (How to treat a drought stressed tree)