My way of "breaking long formula lines in lyx" is to use breqn on demand. The method is demonstrated in this post.
In the LyX "LaTeX Preamble" put the following
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage{breqn}
\newcommand{\breqnoverloadothers}
{%
\renewenvironment{equation}{\ignorespaces\begin{dmath}}{\end{dmath}\ignorespacesafterend}%
\renewenvironment{equation*}{\ignorespaces\begin{dmath*}}{\end{dmath*}\ignorespacesafterend}%
\renewenvironment{multline}{\ignorespaces\begin{dmath}}{\end{dmath}\ignorespacesafterend}%
\renewenvironment{multline*}{\ignorespaces\begin{dmath*}}{\end{dmath*}\ignorespacesafterend}%
}
\newcommand\breqnundefineothers
{%
\renewenvironment{equation}{}{}%
\renewenvironment{equation*}{}{}%
\renewenvironment{multline}{}{}%
\renewenvironment{multline*}{}{}%
}
\AtBeginEnvironment{dmath}{\breqnundefineothers}
\AtBeginEnvironment{dmath*}{\breqnundefineothers}
\AtBeginEnvironment{dgroup}{\def\breqnundefineothers{}\breqnoverloadothers}
\AtBeginEnvironment{dgroup*}{\def\breqnundefineothers{}\breqnoverloadothers}
In Lyx, for long equations for which you want to apply breqn, just 1) typeset the equations using any of math environments that have been overloaded above, i.e., equation/equation*/multline/multline*, and 2) surround the equation(s) using the dmath environment or the dgroup environment, like:
\begin{dmath}
hit ctrl+shift+M to insert a long equation here, and number the equation
\end{dmath}
or
\begin{dgroup}
hit ctrl+shift+M to insert a long equation here, and number the equation
hit ctrl+shift+M again to insert another long equation here, and number the equation
\end{dgroup}
Now you can export to PDF and see that the long equations are handled "automatically" by breqn. Equations not enclosed in dmath or dgroup won't be influenced.
Screenshots are generated but I do not have the 10-point reputation to upload them.