The payment equals about one-third of Cook's annual salary of about $147,000 a year, according to information released by authority board Chairman Don Hutchinson.
Cook left the quasi-public agency in February. The authority manages the county's public parking, golf courses and a skating rink.
"Lynnie’s resignation became official on April 3," Hutchinson wrote in an email response to questions about the severance package. "His notice was accepted during the winter and accrued vacation and holidays took him to that date."
In March, the authority hired Kenneth Mills to replace Cook at a salary of $159,000—about $9,000 more than Baltimore County Executive Kevin Kamenetz. Mills held the same position with the authority nearly 20 years earlier.
It is not clear how the authority determined the size of the payment for Cook.
Hutchinson declined to discuss the issue and did not immediately respond to a request for the agency's severance policy.
"I have given you the information that you originally requested," wrote Hutchinson in an email response. "Beyond the basic information, which should be public information, all other information affecting a personnel decision will rightfully remain confidential."