Hope I'm not duplicating info that's already on the GMB somewhere.
Anyway, I hope the following is helpful:
The R Lalique signatures could be any one of:
wheel cut capital letters(straight lines)
sandblasted capitals using a stencil
stamped capitals using a die stamp
molded capitals in relief on the glass
intaglio capitals molded into the glass
thin diamond-point incised script (often added at the factory when molded mark unclear)
and within these categories there were variations
There was also a mask in a circle used for some powder boxes
and the initials VDA (Verrerie D'Alsace) with the D overlaying the V and A.
(reference Bayer & Waller "The Art of Rene Lalique" which illustrates all these types)
The Lalique workshop at Combs-la-Ville (near Fontainebleau) closed permanently in 1937. The Lalique glassworks at Wingen shut down in 1940 but was reopened in the late 1940s. Rene Lalique died in May 1945 at which time his glassworks had been closed and heavily damaged by the war. His son Marc re-constructed and re-opened the glassworks some years later, and as a mark of respect for Rene it is said that the R in front of Lalique was not used again. In addition the glass used in the new factory had a higher lead content than Lalique glass made before the war. It was full lead crystal with 24% lead compounds, about twice the amount of lead as pre-war Lalique.
I agree that Ascot's piece probably had a lid and Lalique did produce a large number of designs of this kind of box, which were called "Boites et Bonbonnieres" (candy containers?) and ranged in size from 70mm to 255mm (I think that's the diameter - doesn't say).
The pattern on ascot's item looks like a honeysuckle to me, and I couldn't find a honeysuckle pattern in any of my Lalique books nor in the 1932 catalogue.