If the tree can smother the grass underneath it, it will have a better chance of out competing it. On the other hand, the leaves will improve the soil in many ways.
If your trees are small or if your tree doesn't generate a lot of leaves, you can run a mulching mower over the leaves. The pulverized leaves will feed the grass and the tree.
If you have a LOT of leaves, the mulch can end up so thick that is can kill your lawn (and make your tree happy). In this case, you probably want to rake a lot of the leaves. These leaves are great for mulching gardens, shrubs, etc. They are also great in your
compost pile.