A Lord Commissioner did not need a peerage

Did someone need the personal title of Lord to hold the position?

No. The official was a Lord Commissioner because of the office and its delegated authority, not because he already held a peerage.

A naval officer did not have to be a peer, or even a knight, to serve as a Lord Commissioner. The title followed from exercising part of the Lord High Admiral's authority within the commissioned board. It described a constitutional office rather than the holder's inherited social rank. This distinction helps explain why Admiralty titles can look aristocratic even when their occupants were professional officers.