
Not a true answer because a total hack, so therefore just a placeholder because there must be a more elegant solution.
Define the left number command (say) to print both the left and right numbers.
Make a copy of lineno.sty, call it lineno2.sty and put it where TeX can find it (in the current project folder, say).
After line 1523 (% . . . here are the hooks:) add:
\def\LineNumberL{\arabic{linenumber}}%
\def\LineNumberR{\roman{linenumber}}%
Change the next line, defining \makeLineNumberLeft so that it combines both Left and Right definitions together (more or less), that is, change it from
\def\makeLineNumberLeft{%
\hss\linenumberfont\LineNumber\hskip\linenumbersep}
to
\def\makeLineNumberLeft{%
\makebox[-2em]{\linenumberfont\LineNumberL}\makebox[3em]{}%left side
\linenumberfont\hskip\columnwidth
\hb@xt@\linenumberwidth{\hss\LineNumberR}\hss%right side
}%
In the main TeX file, \usepackage{lineno2}.
MWE
\documentclass{article}
\usepackage{lineno2}
\usepackage{lipsum}
\begin{document}
\linenumbers
\lipsum[1-15]
\end{document}