I agree with Bouckeyejoe, grass is going to be hard to grow. Not only for the lack of sun, but also the tree will take up as much water as possible. Here are my two suggestions...

1) Circle the tree to the drip line with 2" of mulch and then find a few full-part shade flowing perennials to plants under the tree. The Tree with live longer and healthier with the mulch and it will much less work for you.

2) Visit your local garden center and ask for shade tolerant ground cover which will stand up to foot traffic.

Good luck...

You might want to try something other than grass. I've seen cast iron plants (Aspidistra elatior) growing under oak trees and in other wide shady spots. At the University of SC, where there are tons of huge oaks and other large trees, they've been using them for years very successfully and with little maintainence effort.

Here is a link that might be useful: more info on cast iron plants

Grass doesn't grow well under oaks -- the oak and the grass will suffer if you try. Also consider that you're on the edge of a lake, if I udnerstood your post correctly. If you're treating the lawn with pesticide and fertilizer on a regular basis, which almost everyone has to do, those materials are running off into the water, adding to pollution levels and reducing oxygen available for aquatic life. Bulbs will do fine under trees, especially early-bloomers which are out before the leaves (narcissus, species tulip, muscari, etc.) and some shade-loving perennials and ground covers, like ajuga, Christmas fern, and epimedium.

Thank you for your responses. I do not treat the non existent lawn with any pesticides or fertilizers...no worries. My concern as posted is:

Right in the middle of the cleared area there is a beautiful oak, not sure of type but it drops TONS of little acorns, which we love for the shade BUT this cleared area is not very large and I'd like to have some grass.

I know that I saw some of the "Steppables" at the nursery last time I was there...I'll have to look into them a bit better. Thanks! (I still do want some grass :)

We have lots of grass under our Southern Red Oak. It drops so many acorns as well as dead branches (probably due to the severe freeze and drought last year)...and the lawn as well as the tree still look great. Just beware of hurting the roots. Aerating the lawn may be good practice every few years since the tree can sometimes make it hard for the grass to breathe.