William Lindow was buried in the Rawlinson family grave, pictured above, in the north-west corner of Lancaster Priory churchyard (next to Lancaster Castle). By marrying Abigail Rawlinson, William - a sea captain for the family - joined Lancaster's principal merchant dynasty in the late 18th/early 19th century. (Inscriptions on the grave detailed here - see entry 435 under Rawlinson, Henry).
The Rawlinson family ships were involved in the slave trade, departing from Lancaster to trade slaves between islands in the West Indies and transport the fruits of slave labour. The slave trade's contribution to the fortunes of families like the Lindows and the Rawlinsons is the subject of Melinda Elder's book The Slave Trade and the Economic Development of 18th Century Lancaster.
According to Global Links' notes on their Lancaster Slave Trade town Trail , William and Abigail had a black servant - probably a slave - called John Chance who worked at their home in Queen Square. The home that 'John' served now houses a doctor's surgery and can be seen in this photo.
In reference to yesterday's post, it seems likely that William Lindow once owned the land now occupied by that area where his name is prominent on street signs. If you view the street map here, you can see the proximity of Lindow Square / Street to their house on Queen Street. I will verify this when I can.