I don't believe Graham is suggesting that no one was making lever watches with draw, but that they were 'luxury goods' for a privileged few, expensive and they certainly were not widespread ...
"the introduction of the lever escapement, first realised by Thomas Mudge in the 1770s, Josiah Emery and others made an extremely limited number of high quality lever watches in the initial period of development between 1782 and 1805.' Camerer Cuss (2009)"
As Chamberlin records the ~30 watches made by Emery cost 150 guineas each. To put this in context, in 1798 it is estimated by Weiss that 120,000 watches were finished in Clerkenwell, each year. How many levers with draw would have been made in 1798? Perhaps ~100. More specifically, how many levers, with draw, would have been purchased by Litherland's target market? I suspect <<10.
We can, I believe, infer some characteristics of Litherland' target market form the advert placed by Litherland, Whiteside & Banning in March 1793 ...
'"The front page advert reproduced on the next page from Gore's Liverpool General Advertiser 29August 1793 (No 1444, Vol XXVII) situated amongst mostly shipping reports, gives an important insight into the perceived market for the new 'Patent' watches that the firm of Litherland, Whiteside and Banning sought. From the published list of watches and prices, it is obvious that most if not all the different variations of layout and finish found in surviving examples were available from the beginning ....
... the advert of the 14 March 1793 issue of Gores was the first to be placed by the firm. smaller, and without the list of watches, it instead promotes the maker's second's beating variant with pirouette (shown in the 1792 Patent) as being 'particularly useful for all astronomical and nautical purposes" Penney June 2012.
It is my belief that Litherland driver was to produce an accurate and reliable watch that he was able to advertise as
A PATENTED HORIZONTAL LEVER WATCH (with all the marketing advantage that carried) having a target price of ~£5, the price of a typical Liverpool watch at the time (price quoted by Dennis Moore in 2001). The suggestion by David Evans (2010) that while Litherland was experimenting with lever designs he
"was unable to devise a suitable safety action, so in desperation geared the balance to the pallet lever. Having tried it, he found it worked remarkably well", makes a lot of sense to me.
John