This MWE should explain the problem and the question:
\usepackage{fontspec}
%\usepackage[ngerman]{babel} % polyglossia is recommended for lualatex
\usepackage{polyglossia}
\setdefaultlanguage[babelshorthands=true,variant=german,spelling=new]{german}
\usepackage[strict=true,autostyle=true,german=quotes]{csquotes}
\usepackage[normalem]{ulem}
\begin{document}
This is what I want to do, but ...
\noindent
... it does not work at all (neither with babel, nor with polyglossia):\\
Aaaaaaa bbbbbbb \uline{cccccccc \enquote{ddddddd} eeeeeeee} ffffffff.
%This is not (exactly) what I want to do (it's just for debugging), but ...
%\noindent
%... it works at least with polyglossia, but not with babel:\\
%Aaaaaaa bbbbbbb \uline{cccccccc "`ddddddd"' eeeeeeee} ffffffff.
%\noindent
%... this works with both:\\
%Aaaaaaa bbbbbbb cccccccc \enquote{\uline{ddddddd}} eeeeeeee ffffffff.
\end{document}