There has been some confusion over the White Lion and the Two Lions. The Two Lions frequently mentioned, was apparently next door to the current Memorial Hall, i.e. the site of the Doric, from back in the 17th century and seemingly the building was there still in the early 19th century. As an extract from Chapman's map of 1787 shows, the White Lion was on its current site then, so they must have been two distinctly separate entities. How long the White Lion was been at its current location has yet to be established.
The history of this property can be traced through documents in the Suffolk Records Office in Bury St.Edmunds, where many deeds regarding this property can be found.
The Two Lions is certainly recorded in 1638. [Mortgage from Robert Austin to John Cottrell] ... dwelling house in tymes past called the Duae Lyons ...] - Deeds held at the Suffolk Record Office
From Millicent Richardson, on her death in 1692 to her son Matthew Richardson of Stradishall; as a marriage settlement in 1788 by Mary Scotman to her son the Revd Thomas Scotman; sold by Robert Lacey in 1816 for £2,100 to Viscount Lowther. When it ceased to be an inn is not clear from these records, but along the way it is referred to as "formerly the Two Lions. Another previous tenant ( pre 1865) was Richard Bedingfield.