I found a mention of a David DOCKRAY, merchant of Lancaster in Vol. 87 of the LCRS (Lancs & Cheshire Records Society publications). Vol.87 is a list of the Free Burgesses of Lancaster, 1688-1840.

It gives this info:

1792/3 DOCKRAY John, son of David of Lancaster, merchant

DOCKRAY Thomas, son of David of Lancaster, merchant

1801/2 DOCKRAY David, of Manchester, manufacturer, son of David of Lancaster, merchant

DOCKRAY Joseph, of Lancaster, son of David of Lancaster, merchant

1806/7 DOCKRAY Benjamin, of Manchester, son of David, late of Lancaster, merchant, deceased

I was also lucky to find an original letter written by Joseph Dockray at Anley House, Settle, to his brother B Dockray, Fenton St, Lancaster, dated 27 Nov 1838.