I have just come across your 2006 enquiry about Heysham Hall. That term can refer to one or other of at least three 19th century buildings. In this case it seems certainly the one which is now the Old Hall Inn.
In the Tithe schedule of 1838 for Heysham the owner of that property is listed as Thomas Rawsthorne, solicitor in Lancaster, and the occupier as Thomas Pennington. Your documentation is the first I have heard of which agrees with this. Thank you. I have for a long time been aware that a Thomas Pennington lived in Lancaster (Castle Hill) in the 1841 census and died later the same year. You mention 'Barrow Greaves'; There is a Greaves Road in Lancaster and a Greaves Methodist Church (foundation date not known to me as yet).
Thomas Rawsthorne himself lived in Heysham, and built (on a previously building site) what was also known as Heysham Hall, round about 1838-40. That building no longer exists, but there are remnants in Heysham Hall Drive and Heysham Hall Avenue today.
See
http://www.heyshamheritage.org.uk/html/higherheyshamoldhall.htmlLater:
Barrow Greaves is a farm to the south of Lancaster,and still appears to be a working farm not engulfed by urban sprawl. It is just on the other side of the M6 where it passes Lancaster University. Heysham Old Hall also had farm buildings as part of it; only in the mid 19th century did Old Hall Farm become a separate entity from Heysham Old Hall with different occupants. Thomas Pennington in the Tithe schedula also 'occupied' significant amounts of land in Heysham which he presumably farmed. At some point in later life (after 1838) he must have moved to Barrow Greaves farm. Does that farm figure anywhere else in your ancestral records?