On page 9 of that same publication is one of the Rolls Royces of the 11th Hussars is shown in the alledged silver and black camouflage. The dark band is much darker than that of the Lanchester unloaded on page 11.
On the MAFVA-page 'British Vehicle Camouflage, 1939-45' http://www.mafva.net/other%20pages/Starmer%20camo.htm
) Mike Starmer and Mike Cooper relate the following:
"1935 1939 In 1936 the 11th Hussars had Rolls-Royce and Crossley armoured cars together with support trucks in Silver with gloss Black disruptive bands. In the same year 6 RTC Vickers Medium tanks were in BS.52 Pale Cream with a fairly standard disruptive pattern of BS.46 Red Oxide applied. By 1937 this pattern had changed somewhat but was the same on every tank and used the same colours. The 11th Hussars meantime had adopted the same cream/ red colours and established a fairly regular pattern on their Rolls-Royce cars. This unit utilised other colours up to 1939 but the pattern remained. By this time various other units in Egypt has also adopted disruptive painting of various styles and colours."
The Lanchesters didn't last long in the desert, being too heavy. The 11th Hussars served in Egypt & Palestine from 1934 to 1939 before being re-equipped with Morris CS9's, but according to several sources left their Lanchesters behind when they went to Egypt in 1934 to relieve the 12th Lancers, who late in 1935 rejoined them bringing 29 Lanchesters, only to leave again by July 1936. This more or less leaves a window of opportunity for desert Lanchesters in said Pale Cream / Red Oxide livery, although they might as well have been of the 12th Lancers. Either way, the desert livery of these cars sounds is interesting enough to keep digging.