Mr. Smarty Plants already has a similar q&a on live oaks leaves. As you can see, this is mostly cons. A few leaves raked into tree wells and maybe a session with a power mower chopping some of them and letting them sift down into the grass will be an advantage to the grass. The thing is, live oaks tend to drop all their leaves at once and that is too much waste material all at once. If they are piled up around tree and shrub bases, fungus may come in and damage the plant, especially if it is rainy or you are watering that bed. Insects will shelter in there, laying eggs and perhaps, like aphids, migrate up to chew holes on the tender young spring leaves.
In addition to all that, there will be acorns that fell in the Fall mixed in there, attracting squirrels, rodents and, again, insects.