Cable Lug Diameter

I think the lug you have is for stranded copper wire.

the extra space is for the gap around the strands.

Can you use a copper lug on a aluminium wire?

Ofcourse, you can use a copper lug for aluminium cable but the opposite should not be done. Cable of larger cross sectional area usually use stranded conductors for better tensile strength. However, Im not clear as to why the lug ID is considerably more than the corresponding cable core diameer.

You are correct in regard to copper lugs on aluminum cable and that the reverse is not recommended. However, in that application the copper lug should be tinned or otherwise plated and a contact aid or sealant, typically containing grit, should also be used to seal the connection. The aluminum strands should be carefully and thoroughly cleaned to remove the non-conductive aluminum oxides before making the connection. (Aluminum rapidly oxidizes on exposure to air). The aluminum strands are normally wire brushed with a SST wire brush in air, wiped with a clean cloth or wiper then a thin coat of contact aid is applied and the surfaces wire brushed again through the contact aid to trap any remaining oxides. Wipe the excess and make the compression.

You don't indicated the stranding but, based on your description, it may not be standard concentric stranded AAC conductor but compression lugs and conductors are matched to the recommended compression dies or tool to achieve specific area reduction ratios.

I will take exception to your reasoning for cables of larger cross sectional area and diameter being stranded for better tensile strength. That's not the reason at all. They are stranded for economy, efficiency and flexibility. Stranded all aluminum conductors will have lower tensile strength than a solid all aluminum conductor of the same cross sectional area. That's also reflected in ASTM standard stranding strength reduction factors. The reason, of course, is that in order to achieve full tensile strength, the strands have to be near-uniformly loaded and that's difficult to achieve when compressive load is transferred to and perhaps through the strands (depending on the number of strand layers). ASCR and other conductors with high strength cores achieve full tensile strength because the core is gripped separately from the outer strands.