I am assuming the Air India flt from HYD - BOM is a DOMESTIC flight.

While Air India as a Star Alliance member now MAY BE able to check ur
bags thru all the way to ATL... HOWEVER... since the Domestic and Int'nl
airport at Mumbai are quite far apart.. the chance of DELAYED baggage
at ATL may become an issue.. so I suggest.. u just check ur bags thru
to MUMBAI.. retrieve them and RE-check at the LH counter for the onward journey... just a suggestion... have a safe journey