My quoting
package provides a consolidated environment for displayed text with control over first-line indentation. Without LyX, one simply doesn't add a blank line before the start of the environment and hereby prevents indentation:
\documentclass{article}
\usepackage{quoting}
\newcommand*{\sometext}{Hello, here is some text without a meaning. This
text should show, how a printed text will look like at this place.
If you read this text, you will get no information.}
\begin{document}
\sometext
% <-- No indentation of first `quoting` line
\begin{quoting}
\sometext
\sometext
\end{quoting}
\sometext
\end{document}
With LyX it may be difficult to avoid "blank lines", but you may use the indentfirst=false
option when adding the package to your LaTeX preamble:
\documentclass{article}
\usepackage[indentfirst=false]{quoting}
\newcommand*{\sometext}{Hello, here is some text without a meaning. This
text should show, how a printed text will look like at this place.
If you read this text, you will get no information.}
\begin{document}
\sometext
\begin{quoting}
\sometext
\sometext
\end{quoting}
\sometext
\end{document}
Output for both examples:

\noindent
? I don't know if it's possible to write it on LyX, nor if it's possible to set a macro using it for the first paragraph.