James Lyne Hancock was the son of James Hancock and Elizabeth Lyne, and a member of the Hancock family of Marlborough, England. The Hancocks were a significant British family in the eighteenth and nineteenth centuries, known for their contributions to science, art, and industry.

James Lyne Hancock is best known for his work in the rubber industry and his company, James Lyne Hancock Ltd, which was situated at Goswell Mews, North London. James Lyne Hancock was initially responsible for running the Goswell Mews works for his uncle Thomas Hancock. The pair were involved with C Macintosh & Co., another manufacturer of rubber products, but Thomas Hancock split off his part of the business and sold it to his nephew c1842-5. Lyne Hancock then installed moulding and vulcanising facilities at the site, and began producing rubber and vulcanised rubber products under the company name James Lyne Hancock Ltd.

In the 1870s, James Lyne Hancock made his first round rubber tyre for the Ariel bicycle of Haynes and Jeffries; this used soft spongy rubber on the underside and toughened rubber on the tread, an idea which has been copied in the tyre trade ever since, even with pneumatic tyres.