I was using the following preamble with lualatex. I have many sanskrit words using unconventional Roman script, such as ahaḿtattva, rúpa, tanmátra.
\documentclass[12pt, b5paper]{book}
\usepackage{fontspec}
It worked well with the default font, until I changed to a new font:
\setmainfont{Calluna-Regular}
All the special characters previously worked out fine now all disappeared. Instead, I get warnings such as:
LaTeX Font Warning: Font shape `EU2/Calluna-Regular(0)/m/sl' undefined using `EU2/Calluna-Regular(0)/m/n' instead on input line 11.
If I typeset each character manually, such as \'{a}, \'{u}, then I can get the special characters back. But doesn't work in \'{m}, nothing shows. With \'{t}, only normal t will show.
When compiling with XeLaTeX, some special characters, such as á, can show correctly. I'd prefer to use LuaLaTeX for its better microtype support.
Is that because the font I've chosen does not support these special characters? But it does support \'{a}, \'{u}, etc. Why doesn't it print these characters by itself as in default font?
Can I redirect the font table to correct font instead? If so, how to do that?
I cannot use the Sanskrit support in polyglossia, because I'm using a different Roman script.
I would like to stick to the new font, compile with LuaLaTeX, and show all the special characters correctly.

\'{}. But Calluna (even the version you have to pay for) has no ḿ; unless you want to play with combining accents, you should choose a font with the characters you need. – Thérèse Sep 03 '15 at 18:27\setmainfont{Calluna}[Contextuals=Alternate]. – Thérèse Sep 03 '15 at 18:29áandú, I get the characters. However, the font also missesḿ(U+1E3F). My advice is to use a different font. You may consider Erewhon, for instance, that's distributed with TeX Live and MiKTeX. – egreg Sep 03 '15 at 19:43\accent"00B4 m, but it's vastly preferable to either have the combining accent or the precomposed glyph. – egreg Sep 03 '15 at 20:18\documentclass{...}and ending with\end{document}. – Martin Schröder Sep 04 '15 at 12:56