Hi Lewis S ...I 'm pretty sure that I have , or have seen a photo of this small generator for heating the flying suits ,..Can I find it remains the question !.
The Rifle stock as mentioned , would be the standard Mk1 infantry Lewis gun shoulder stock ....On the adjustable " Swan neck " , for the purpose of safe stowage , there is fitted a spring clip and 1/2" wide webbing Haft with buckle for securing it when not required . There is a " Demonstration photo" in the Datafile (RAFM photo ) of its use , but I don't think that I have seen a photo of a Lewis with the shoulder stock on opperational service .( Have to go thru' photos )
Unlike machines with fixed ( Eg..Vickers ) machine guns ,; The free mounted Lewis were mostly kept and issued by the armourers according to opperational requirements , and are unlikely often, to have been kept ON the machines . It is possible that an individual of some standing , could have his " own " MG . or request on with the shoulder stock . ...This would not be a lot of use in the front mounted position however, ..too restrictive of movement .
Best I can do on this I'm afraid . Regards John