In natural settings, grass and trees do not coexist easily. There is not much grass in a forrest and there are not many trees in natural meadows. It is also not very healthy for the trees or the grass. If you intend to buck the natural system and try growing grass under trees, the grass will need a large amount of filtered or direct sunlight through or under the branches.
Therefore, properly and regularly pruned trees will have a better chance of growing grass under them. Be aware that it may take a while for grass to become established, and because of the growth pattern of some trees, no grass will be able to grow under them. In which case properly established and maintained mulch beds are strongly recommended.
Posted in: Tree Pruning Questions