Lineno for 2 column

Use the switch option for the lineno package.

\documentclass[twocolumn]{article}
\usepackage[switch]{lineno} 
\usepackage{lipsum} %Creates example text
\begin{document}
\linenumbers
\lipsum[1-20]
\end{document}

Simply add [columnwise] in the options of the package:

\usepackage[switch,columnwise]{lineno}

The following is a partial solution.

\documentclass{article}
\usepackage{multicol}
\usepackage{lineno} 
\usepackage{lipsum}
\begin{document}
\begin{multicols}{2}
\linenumbers
\lipsum[1-1]
\columnbreak
\rightlinenumbers
\lipsum[1-1]
\end{multicols}
\end{document}