I pulled out my copy of "Nelson's Navy" by Brian Lavery -- a wonderful (and I believe authoritative) reference work. (My husband got me this when I was in the throes of my Patrick O'Brian obsession.) This books says marine lieutenants were promoted by seniority only (see final sentence below). I'm quoting most of the paragraph on these officers, as I think folks will find it interesting.

"In some ways the position of marine lieutenants was anomalous aboard ship. They were clearly junior to naval lieutenants, and therefore to masters, who were only warrant officers, while the marine lieutenants were commissioned officers. The Admiralty Regulations recognised this dilemma.... Though their economic status was no greater than that of a warrant officer, they were allowed all the privileges of commissioned status, with their own cabins and access to the wardroom and quarterdeck.... Marine officers were appointed by the Admiralty, largely through influence. They did not purchase their commissions like army officers; promotion was strictly by seniority and tended to be rather slow." (Page 150)