The spelling of the name of Lawrence Brockett is given as "Laurence" on the web site of The Thomas Gray Archive (http://www.thomasgray.org), but as "Lawrence" everywhere else.
For examples on the Interent, see: http://www.countryhousehotels.co.uk/history.htm http://www.bartleby.com/220/0614.html
From other (non-Internet) information, I also believe that the w spelling is correct so I am correcting this page accordingly.
EdH