Cross referencing to any reference counter without adding labels

Question

This answer provided a great solution for creating a new reference counter. I have a further idea to refer to a particular point without putting label or ref manually. This is done in package linguex for a different purpose. Let's see this code.

\documentclass{article}
\usepackage{lipsum}
\usepackage{amsmath}
\usepackage{linguex}
\newcounter{mynumber}
\newcommand{\myno}[1]{\hfill\refstepcounter{mynumber}(\arabic{mynumber})\label{#1}}

\begin{document}
\lipsum[1]
\ex. This is one example.

\lipsum[1]
\ex. This is another example.

Example \LLast illustrates abc and \Last illustrates xyz.

\section{New section}
This is my first theorem. \myno{first}\\
This is my second theorem. \myno{}\\
By \eqref{first} it is evident that bla bla bla.\\
By \eqref{} it is evident that bla bla bla.\\
\end{document}

This code will produce -

Now as the linguex package provides me commands like \Last, \LLast I want them to be for these new ref-counters. Is it possible?

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This is a pseudo code made by me. It looks almost the same, but has two additional commands which should end-up in referring to the theorem-numbers in an automated way. The expected output is exactly the same like the screenshot attached.

\documentclass{article}
\usepackage{lipsum}
\usepackage{amsmath}
\usepackage{linguex}
\newcounter{mynumber}
\newcommand{\myno}{\hfill\refstepcounter{mynumber}(\arabic{mynumber})}

\begin{document}
    \lipsum[1]
    \ex. This is one example.

    \lipsum[1]
    \ex. This is another example.

    Example \LLast illustrates abc and \Last illustrates xyz.

    \section{New section}
    This is my first theorem. \myno\\ % Note that I have no compulsory label argument here. It is automatically labelled.
    This is my second theorem. \myno\\
    By \NewLast it is evident that bla bla bla.\\ % Here the labels are referred.
    By \NewLLast it is evident that bla bla bla.\\
\end{document}