It is possible that John Lack and later his widow, were running this house pre 1744.

Recorded as the OSTRICH in Holkham Estate records to at least 1787.
Found in publications as the LEICESTER ARMS from at least 1768.
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March 19th 1776 - Robert Russell of Holkham butcher, ......... to pay debts to Mr Bell who will give his personal attendance on Monday 1st day April next at the OSTRICH in Holkham. ~
The Norfolk Chronicle of 13th July 1776 advertised
` Thomas Brett returns his friends his most sincere thanks for past favours.........has this summer made addition to his lodgings.'

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HOLKHAM - LEICESTER ARMS June 1777 Thomas Brett returns his Friends his most sincere thanks for the many Favours he has already received and humbly solicits their future commands: Begs leave to inform them and the Publick in general that he provides as usual viz. for Mondays and Tuesdays makes up sixteen Beds; and that his greatest assiduity may be depended on to render his House agreeable.

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Holkham Nov.22, 1783. William Fodder begs Leave to inform the Public in general, that he has take the OSTRIDGE INN, near Holkham Hall, which he has fitted up in a particular Manner for the Accommodation of Ladies and Gentlemen who shall take the Norfolk Tour; He has also laid in a Stock of Wines and Spirituous Liquors of that Quality which he hopes together with his Attention to oblige, will give Satisfaction to all those who will please to favour him with their Company, whose favours will be gratefully acknowledged. ~
20 August 1792. To be sold at HOLKHAM INN, the Holkham flock of Norfolk ewes . In lots from 20 to 50.

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Note that Joseph Boulter is named at the LEICESTER ARMS in 1846, but the NEW INN in the 1847 Register of Electors and in the 1851 census. 
The NEW INN had been built in 1786-7 by Coke of Norfolk, seemingly replacing this house.