https://www.recreation.gov/permits/4251909

Note that the application fees are separate from the permit itself as well:

Application Fee: A non-refundable $9.00 lottery fee is required for each lottery application.

Recreation Fee: If selected in the lottery, a recreation fee of $7.00 per person or dog is required. This fee is paid online when filling in additional information to complete the process after successfully winning. Everyone, regardless of age, must be included in the permit. This includes infants that are not walking. Payment of recreation fees is only required if a permit is awarded through the lottery.