Quote

At this assizes, an action having been brought against the Gunner at Cowes Castle, for firing a nine pounder at Capt. Footner’s vessel, at the entrance of Cowes Harbour, in order to sink her, for not complying with the Gunner’s demand of 4d. for an anchorage; it being clearly the opinion of the Judge and Jury that the Gunner had no right to enforce a demand with cannon, loaded with ball, levelled at the ship, a verdict was given for the plaintiff, with 10l. damages.

— Hampshire Chronicle, Monday 08 March 1773 source

The following two references bookend the assizes nicely, giving us a possible name for the vessel:

Quote

PORTSMOUTH, Sept 10.

Since my last arriv’d at this port, the Dick and Richard, Woolver, from Penzance; London, Johnson, Lymington, Footner

Hampshire Chronicle, Monday 14 September 1772 source

Quote

SHIP NEWS

PORTSMOUTH, July 22, Arrived the Lymington, Wm. Footner;

Hampshire Chronicle, Monday 26 July 1773 source

Best video I could find.