Lively, <-1797->
Type: Revenue cutter ; Armament : 8
Tons : 165
Notes:

N.B. These notes may well cover more than one vessel.

5 Jun 1797 captured the French privateer Flying Fish off Shoreham.
The following appeared in the London Gazette : www.london-gazette.co.uk/issues/14017/pages/535
Copy of a Letter from Mr. F. Newport, Colledor of HM Customs at Dover, to Evan Nepean, Esq; dated June 5, 1797.
Sir, I Beg Leave to inform you, that Mr. Dubois Smith, Commander of the Lively Cutter, in the Service of the Customs, sent in this Morning a French Lugsail Privateer, called the Flying Fish, which he took off Shoreham, with Two Swivel Guns, a Number of Musquets, and Twenty-four Men; out Three Days from Morlaix, and had taken nothing. I am, Sir, &c. &c. &c. F. Newport.

1 Jan 1799 Commander = D Smith ; 18 men ; station : Kent, Sussex and Essex.

13 Aug-Oct 1799 employed on expedition to Holland.

28 Aug 1799 capture of the Dutch hulks Drotchterland and Brooderschap, and the ships Helder, Venus, Minerva, and Hector, in the New Diep, in Holland.

13 Feb 1801 Lively, Viper, and Argus (revenue cutters) captured the French privateer Sans Peur in the North Sea.

24 Feb 1802 prize money resulting from the capture of the Dutch hulks Drotchterland and Brooderschap, and the ships Helder, Venus, Minerva, and Hector due to be paid.

17 Nov-30 Dec 1802 prize money resulting from the expedition to Holland due for payment.

Lively, <-1805-1815->
Type: Revenue and / or Excise Cruiser ; Armament 10
BM: 121 tons
Complement : 32
Notes:

N.B. These notes may well cover more than one vessel.

May 1805 London to Beachy Head - Vessel of Port of London.

7 Mar 1807, when in company with the Revenue cruiser Tartar, were fired on by the crew of a smuggling lugger in Folkstone Roads. See www.london-gazette.co.uk/issues/16011/pages/343

Whitehall, May 8, 1807.
Whereas it has been humbly represented to the King, that on the Night of the 16th Ultimo, a Lugger, laden with smuggled Spirit and other contraband Articles, having been chaced on Shore opposite the Town of Folkestone, in Kent, and boarded by the Boat's Crew of the Lively Cutter, in the Service of the Revenue of Excise, William Lilburn, Commander, a great Number of Persons assembled riotously, and fired several vollies of small Arms against the said Lugger and the Officers therein, and a Cannon-shot also struck and damaged her.
His Majesty, in order to bring to Justice Persons who have been guilty of this violent Outrage and Capital Felony, is pleased hereby to promise His most gracious Pardon to any Accomplice who shall discover any one cr more of the said Offenders, so that he or they may be apprehended and convicted.

Dover 13 Jan 1811 The Lively custom-house cutter struck the South Pier Head, and the stove her bows, when veering round the North Pier Head, and sank ; her crew were rescued.

Per Navy List circa 31 Dec 1814 shown to be armed with 10 guns as an Excise cruiser under the command of Wm. Lilburn, and responsible to the English Board.

Dover 8 Nov 1815 Has taken and sent in a boat laden with foreign spirits.

NB I have no knowledge regarding when vessels were built or broken up for the Revenue Service, so these notes may well cover one or more vessels.