Another reason not to use linguex. :) If you're not committed to it, I would recommend gb4e instead. But if you are committed to it, you can do what you want by using the cgloss4e glossing macros directly rather than the linguex wrappers.
Using linguex alone
Because linguex adds a small vertical space in the \ex. line, I've made a corresponding \ix. command to use when an example has the introduction line. If you like the small extra space (as in the second version of my sample code) then you don't need the \ix. command at all.
\documentclass{article}
\usepackage{linguex}
\def\ix.{\ex.\setlength{\Extopsep}{0pt}}
\begin{document}
\ix.
\a. This is an introductory sentence describing the context.
\gll This is a gloss\
This is another gloss\
\glt `This is a translation.'
\ex.
\a. This is an introductory sentence describing the context.
\gll This is a gloss\
This is another gloss\
\glt `This is a translation.'
\end{document}

Using linguex with cgloss
If you are also using cgloss, then the solution actually turns out to be simpler, we just need to add a zero length \vskip to the \gll command, which we can do using the etoolbox package.
\documentclass{article}
\usepackage{linguex,cgloss}
\usepackage{etoolbox}
\pretocmd{\gll}{\vskip0pt}{}{}
\begin{document}
\ex.
\a. This is an introductory sentence describing the context.
\gll This is a gloss\
This is another gloss\
\glt `This is a translation.'\hfill (Language information)
\end{document}

cglossinstalled on the machine I wrote the answer on and assumed it wouldn’t make a difference. I’ll take a look. – Alan Munn Apr 10 '22 at 00:01cglosssolution turns out to be simpler, and I've updated the answer but I've kept thelinguexsolution in the answer as well for those who might not be usingcgloss. – Alan Munn Apr 10 '22 at 03:33\vskipamount to something greater than0pt.cglossdefines a\gltoffsetmacro (default is0pt) which will put space between the gloss and the translation. If you you use\gltoffsetas the value you use for the\vskipin the adjusted\gllcommand you can have equal space above and below. N.B.\gltoffsetis a macro not a length, so you set it with\renewcommand{\gltoffset}{...}not\setlength. – Alan Munn Apr 10 '22 at 23:00