Would the solid material inside an airship displace air and be counted towards lift? The hydrogen inside an airship has a mass that is approximately 14 times lower than the mass of air and this difference results in lift.

However the solid material inside an airship including the frame, skin, walkways, gasbag material etc. would also displace air.  Would the air that these materials displace also be counted towards lift?  I'm not sure.
If the extra displacement is counted towards lift is there any reasonable estimate as to how much space the solid material might fill?  1%, 2%, 5%?
A U Class Zeppelin has an outside volume of approximately 59,000 cubic meters.  However if 2% of this volume was solid material that's 1,180 cubic meters of atmosphere displacement or an extra 1,445 Kg of lift.  Although not decisive I'm sure that any little bit helps.
It would, but it is so little it is not noticeable
Duraluminium has a density of 2780 kg/m3, plain air has a density 1.3 kg/m3. So the buoyancy is in the order of 0.05%. The dry weight of the Hindenburg for example was 100 tons, meaning that the buoyancy of the solid material is about 50 kg.
This is so little that other effects on lift — i.e. changes in temperature, internal gas pressure, external atmospheric pressure, dynamic lift from relative wind speed, ballasting, spending fuel, and more — will completely drown out this effect.