Too early for Lloyd's, but there were precursor registers apparently.
From Lloyd's registry website: "In 1760, the Register Society was formed by the customers of the coffee house. The Society printed the first Register of Ships in 1764 in order to give both underwriters and merchants an idea of the condition of the vessels they insured and chartered.
"In 1834, the organisation was reconstituted as Lloyd's Register of British and Foreign Shipping, and the first 'Rules' for the survey and classification of ships, were published. Sixty-three surveyors were employed in the first year and by 1840, 15,000 vessels had been surveyed in accordance with the Rules. In 1852, the organisation opened its first overseas office, in Canada, and other offices followed around the world. By 1914, the organisation became simply 'Lloyd's Register of Shipping' in recognition of its international status. In the 1900s we began to apply our expertise developed in the marine industry to other industrial sectors resulting in today's wide ranging services."