I realise that this is an old post. I found it when searching for Allendale-related posts and was intrigued by the fact that it has been viewed hundreds of times but without response. So, it was a challenge. I'm responding now in case someone else is looking for information on Lot Head. (davidft has not posted for some time)
I've concluded that Lot Head was the site marked as Allotment Head near Elpha Green on this map. Allotment Head is over to the left, I chose this zoom to include Elpha Green and Spartylea (Swinhope Mill is slightly to the south). And Sinderhope, mentioned by the OP is about 2 miles to the north.
https://maps.nls.uk/geo/explore/#zoom=15.9&lat=54.83331&lon=-2.24446&layers=257&b=ESRIWorld&o=100My conclusion is based upon the history of Elizabeth Philipson (full census entries not included, just a couple of names where relevant).
1861
Lott Head, John, 30, and Elizabeth Philipson 30 [John 7 mo.]
1871
Lotment Head, Elizabeth Philipson, widow, 40 [John 10]
1871 marriage John Pigg, Elizabeth Philipson
1872 birth of Emily Ann Pigg
1881
Lot Heads, Elizabeth Pigg, married, 50 [no sign of Mr Pigg here and I have not tried to find him]
1891
Allotment Head, Elizabeth Pigg, married, 60 [still no sign of Mr Pigg]
1901
Lot Heads, Emily Pigg, 28 [I have not located Elizabeth in 1901]
1908 probate Elizabeth Pigg of
Lothead, Swinhope Allendale, to John Philipson blacksmith
All of the above census entries are close to entries for Elpha Green, Swinhope Mill etc.
20 September 1902: Newcastle Journal
A report of the Sheep Show at Allenheads mentions, under the heading of Shorthorned Cattle, for farmers whose acreage does not exceed 25 acres, Mrs Philipson of Lot Head.
20 April 1985: Newcastle Journal
a reference to Grass Park Lets at Hexham Auction Mart mentions Elpha Green and Lot Head, Spartylea.