According to Lloyds Register of shipping the vessel LIVELY, owned and captained by Dobson was classed as a Brig (Brigantine) home port, Shields. (South/North Shields) Up until 1841 Shields ships were registered in Newcastle.
It maybe worthwhile to contact Tyne and Wear Archives to see if they have anything on the1797/1798 Muster Roles (Early Logbooks) and/or movements of LIVELY during this period. Be aware there were over 20 ships with the name LIVELY. around in 1797/1798.
I don't know if you have reserched these records from London Metropolitan Archives. Re Calendars or lists of prisoners 1796-1797,
https://search.lma.gov.uk/SCRIPTS/MWIMAIN.DLL/182928473/2/3/80?RECORD&UNION=Y#coll3regards
SW