From the New-York Evening Post, Saturday, 4 August 1804, p. 3:

Arrived [inter alia] ship LIVE OAK, Dyer, [from] Londonderry, 41 days.

The ship LIVE OAK, from Londonderry, with some linen and 63 passengers, to Jacob Barker. Sailed in co[mpany] with the British ship DUNCAN, Sibson, for New York. Left, the ship WM. LITTLE JOHN, Forrest, time of sailing uncertain. Cabin passengers, Capt. Archibald M'Corkell, Mr. John Murdoch, and Mr. Abraham Ludlow, of this city. On Thursday evening about 7'oclock, 7 miles from the light house and 2 leagues from the high-lands of Neversink, the LIVE OAK was taken possession of by the British ship LEANDER, brought to anchor and detained till 10 o'clock yesterday morning; during which time they pressed about 40 of the passengers, and one seaman, some of whom were separated from their parents, and others leaving considerable property on board the LIVE OAK. The LEANDER, running under the stern of the LIVE OAK, carried away part of the stern.

Lloyd's Register of Shipping for 1811 lists no fewer than 31 sailing vessels with the name LIVELY:

1. Ship LIVELY, R. Fenwick, master, 320 tons, single deck with beams, built in Sunderland, in her 12th year [in 1811], owned by E. Watt, surveyed at London, destined voyage Quebec
2. Brig LIVELY, J. Graham, master, 158 tons, single deck with beams, built in Workington, in her 26th year [in 1811], owned by Thompson, surveyed at Liverpool, destined voyage Quebec
3. Brig LIVELY, J. McBride, master, 115 tons, single deck with beams, built in Ayre, in her 3rd year [in 1811], owned by Cowan & Co., surveyed at Greenock, destined voyage Quebec

The U.S. ship LIVERPOOL was built at New York by Brown & Bell, in 1843. 1077 tons; 175 ft 6 in x 36 ft 6 in x 22 ft 3 in (length x beam x depth of hold). She had the longest continuous line service of any sailing packet:

• 1843-1849 in the New Line between New York and Liverpool
• 1849-1855 in the Blue Swallowtail Line between New York and Liverpool
• 1855-1880 in the Red Swallowtail Line between New York and London

Source: Robert G. Albion, Square-riggers on Schedule; The New York Sailing Packets to England, France, and the Cotton Ports (Princeton: Princeton University Press, 1938), pp. 280-283.

From Lloyd's Register for 1820:

Ship LIVERPOOL PACKET
J. Birkett, master
376 tons
built Boston, in her 9th year
owner: McCalmnt
draught when loaded: 16 feet
port of survey: Liverpool
destined voyage: Philadelphia