If you look at the status bar (bottom of the LyX window) when you click the appropriate menu item, you'll see the function appear there for a second or two. The two functions you're after are
script-insert superscript
script-insert subscript
The Problem lies within the definition of \textsuperscript that uses math mode.
\DeclareRobustCommand*\textsuperscript[1]{%
\@textsuperscript{\selectfont#1}}
\def\@textsuperscript#1{%
{\m@th\ensuremath{^{\mbox{\fontsize\sf@size\z@#1}}}}}
A possible workaround is redefining the actual command so that it will not get in the way with your equations, this needs graphicx:
\renewcommand{\textsuperscript}[1]{\raisebox{0.8ex}{\scalebox{0.66}{#1}}}
Or this needs relsize
\renewcommand{\textsuperscript}[1]{\raisebox{0.8ex}{\smaller{#1}}}
I admit that this is just an easy workaround emulating the typrsetting of superscripts. It might be possible, that modern typography defines super/subscript in a certain way.
This also works with various enlargements of text sizes. This MWE also emulates a textsubscript:
\documentclass[12pt,oneside,letterpaper,titlepage]{article}
\DeclareMathSizes{12}{20}{14}{10}
%% Solution 1
\usepackage{relsize} %smaller
\renewcommand{\textsuperscript}[1]{\raisebox{0.8ex}{\smaller{#1}}}
\newcommand{\textsubscript}[1]{\raisebox{-0.4ex}{\smaller{#1}}}
%% Solution 2
%%\usepackage{graphicx} %scalebox
%%\renewcommand{\textsuperscript}[1]{\raisebox{0.8ex}{\scalebox{0.66}{#1}}}
%%\newcommand{\textsubscript}[1]{\raisebox{-0.4ex}{\scalebox{0.66}{#1}}}
\begin{document}
...modulation by Ca\textsuperscript{2+}...
...soluted in water H\textsubscript{2}O...\\
\tiny Ca\textsuperscript{2+}
\scriptsize Ca\textsuperscript{2+}
\footnotesize Ca\textsuperscript{2+}
\small Ca\textsuperscript{2+}
\normalsize Ca\textsuperscript{2+}
\large Ca\textsuperscript{2+}
\Large Ca\textsuperscript{2+}
\LARGE Ca\textsuperscript{2+}
\huge Ca\textsuperscript{2+}
\Huge Ca\textsuperscript{2+}
\normalsize
\begin{equation}
\sigma^2 = iI - \frac{I^2}{N}
\end{equation}
\end{document}
Further reading relsize and graphicx.
For chemistry typesetting (I guessed that on the calcium bit) there are some packages available, like bpchem or mhchem, that handle formulas quite well.
Best Answer
You can use
\textsuperscript{th}. It sets its contents in text mode and can be used in math or text mode.