Stop Giving Big Oil Free Money Act of 2019 This bill prohibits the Department of the Interior from issuing new oil or natural gas production leases in the Gulf of Mexico to any person who does not renegotiate certain existing leases to require royalty payments if the price of oil and natural gas is greater than or equal to specified price thresholds. Interior must also, upon request, agree to amend any lease issued for any Central and Western Gulf of Mexico tract during the period of January 1, 1996, through November 28, 2000, to incorporate specified price thresholds.