You can use running linenumbers which are reset to 1 for each paragraph. The reset can be automated using a hook to the \par
command (which also works for paragraphs created by empty lines).
MWE:
\documentclass{article}
\usepackage[excludeor]{everyhook}
\usepackage[running]{lineno}
\runninglinenumbers
\PushPreHook{par}{\resetlinenumber[1]}
\begin{document}
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque
\end{document}
Result:

The same result can be obtained with \AtBeginDocument
, as follows:
pdflatex "\AtBeginDocument{\RequirePackage[excludeor]{everyhook}\RequirePackage[running]{lineno}\runninglinenumbers\PushPreHook{par}{\resetlinenumber[1]}}\input{mydocument.tex}"
of course provided that mydocument.tex
is something like
\documentclass{article}
\begin{document}
Lorem ipsum dolor ...
\end{document}