A better way is to use \textup, not \text or \mbox.
\documentclass[11pt,a4paper,oneside]{report}
\usepackage[T1]{fontenc}
\usepackage{fouriernc}
\usepackage{mathtools}
\usepackage{amssymb,amsthm}
\usepackage[a4paper, hmargin={3.5cm,3cm}, vmargin={2.5cm,2.5cm}]{geometry} %margin
\usepackage{ marvosym }
\newcommand\blitz{\textup{\Lightning}}
\begin{document}
\section{The {\Lightning} Symbol in Math Mode is (\blitz^{\blitz^\blitz})}'
\begin{equation}
\Lambda\gamma \blitz_{\blitz_\blitz}
\end{equation*}
\end{document}

If you want to use it as an operator, additionally wrap it in \mathbin{\textup{\Lightning}} or \mathrel{\textup{\Lightning}}, etc. If you do not want the symbol to appear bold in bold headers, use \textnormal instead of \textup. (I don’t believe this does anything for marvosym, but it would for many other symbol fonts.)
If you use \text, the symbol will be formatter to match the surrounding text—for example, it will switch to italics if used in an italicized theorem statement. If you use \mbox, it will not scale in superscripts or subscripts.
In LuaLaTeX or XeLaTeX, you should use the ☇ (U+260 Lightning) or ⚡ (U+26A1 high voltage) Unicode symbols from a font that contains them, e.g.
\documentclass[11pt,a4paper,oneside]{report}
\tracinglostchars=2
\usepackage{mathtools}
\usepackage{amsthm}
\usepackage{unicode-math}
\setmainfont{TeX Gyre Schola} % Clone of the New Century Schoolbook font used in fouriernc
\setmathfont{TeX Gyre Schola Math}
\newfontfamily\symbolfont{DejaVu Sans}[Scale=MatchUppercase]
\newcommand\textblitz{{\symbolfont\symbol{"26A1}}}
\newcommand\mathblitz{\textup{\textblitz}}
\usepackage[a4paper, hmargin={3.5cm,3cm}, vmargin={2.5cm,2.5cm}]{geometry} %margin
\begin{document}
\section*{The {\textblitz} Symbol in Math Mode is (\mathblitz^{\mathblitz^\mathblitz}) }
[ \Lambda\gamma \mathblitz_{\mathblitz_\mathblitz}
]
\end{document}
