It seems that, if I want to use the letters and digits from a system font that is not especially designed for mathematics in math mode as well, I need mathspec and XeLaTeX; and cannot replace XeLaTeX with LuaLaTeX (with which mathspec is incompatible). Is that right?
Yes. If you want to use
mathspec, then at present you need to run XeLaTeX. (The
mathspec package pre-dates wide availability of LuaTeX.)
There are few technical reasons for this, but
mathspec does use one primitive that would need to be emulated in LuaTeX before it could fully supported:
\XeTeXglyphbounds— this is used in the
"definitions to provide better kerning between "faked" maths symbols.
Besides this, the main features of the package could be fairly easy translated into LuaTeX-compatible code, however. Unfortunately the developer of
mathspec no longer has the time to work on the code.
I believe the
mathastext package performs a similar role as
mathspec but is compatible with both XeTeX and LuaTeX. I haven't done a direct comparison of their feature sets, however.