Q.Grass under tree
If I want grass this season and beyond ,could I till the dead area then put down sod now , early July?

When to seed or sod your garden can depend on your growing zone.
Soil prep is key to success for either seed or sod.
https://www.gardeningknowhow.com/ornamental/trees/tgen/tips-for-growing-grass-under-a-tree.htm
https://www.gardeningknowhow.com/lawn-care/lgen/lawn-seeding-tips.htm
https://www.gardeningknowhow.com/lawn-care/lgen/installing-sod-instructions.htm
You may also want to contact your County Extension Office for a list of regional grasses to use on your lawn.
https://www.gardeningknowhow.com/extension-search/