Don't know where you are, or what species of oak you are concerned about. Where I am, the native oak is Quercus garryana. It, and the similar Quercus kelloggi are adapted to summer drought. People do plant and water lawns underneath them, but the received wisdom is that, over a period of years, this will increase their susceptibility to fungal disease, and shorten their lives. The received wisdom is also that seedlings of these oaks will adapt better to summer irrigation than mature specimens. I have no data sources confirming these ideas however.
There are many species of oak in the world, and many have evolved in summer-wet areas and in swamps. If you know which oak you have, and where it evolved, you can make a pretty educated guess about its moisture tolerances.
AFAIK, no oak secretes a plant-killing substance as walnuts do. Oak leaves can mat down and form an almost impervious layer, which effectively prevents most other plants from growing. Just break the mat up. Shredded oak leaves are good as mulch and in
compost.
