This answers a question addressed to me in comments.
You have done everything you need to do. You don't need to do anything special to use the fonts beyond adding the lines you mention to your preamble.
Here's a complete example:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{lxfonts}
\usepackage{kantlipsum}
\begin{document}
\kant[1-20]
\end{document}

If you want to only use the fonts within the special environment, then you can activate them for text just within its scope by copying relevant parts of lxfonts.sty. Note that this will still change the maths fonts globally.
\documentclass[12pt,letterpaper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsfonts,mathtools,nicefrac}
\usepackage{xcolor}
\definecolor{examplecolor}{gray}{0.4}
% font configuration adapted from lxfonts.sty
\input{ulmsa.fd}
\input{ulmsb.fd}
\newenvironment{exampletext}{%
\renewcommand\rmdefault{llcmss}%
\renewcommand\sfdefault{llcmss}%
\renewcommand\ttdefault{llcmtt}%
\noindent\large\color{examplecolor}%
}{}
\SetSymbolFont{operators}{normal}{OT1}{llcmss}{m}{n}
\SetSymbolFont{letters}{normal}{OML}{llcmm}{m}{it}
\SetSymbolFont{symbols}{normal}{OMS}{llcmsy}{m}{n}
\SetSymbolFont{largesymbols}{normal}{OMX}{llcmex}{m}{n}
\SetSymbolFont{operators}{bold}{OT1}{llcmss} {bx}{n}
\SetSymbolFont{letters} {bold}{OML}{llcmm} {bx}{it}
\SetSymbolFont{symbols} {bold}{OMS}{llcmsy}{bx}{n}
\SetSymbolFont{largesymbols}{bold}{OMX}{llcmex}{m}{n} % no bold!
\DeclareSymbolFontAlphabet{\mathrm} {operators}
\DeclareSymbolFontAlphabet{\mathnormal}{letters}
\DeclareSymbolFontAlphabet{\mathcal} {symbols}
\DeclareMathAlphabet {\mathbf}{OT1}{llcmss}{bx}{n}
\DeclareMathAlphabet {\mathsf}{OT1}{llcmss}{m}{n}
\DeclareMathAlphabet {\mathit}{OT1}{llcmss}{m}{sl}
\DeclareMathAlphabet {\mathtt}{OT1}{llcmtt}{m}{n}
\SetMathAlphabet\mathsf{bold}{OT1}{llcmss}{bx}{n}
\SetMathAlphabet\mathit{bold}{OT1}{llcmss}{bx}{sl}
\SetSymbolFont{AMSa}{normal}{U}{lmsa}{m}{n}
\SetSymbolFont{AMSb}{normal}{U}{lmsb}{m}{n}
\makeatletter
\xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F%
\mkern-14.2mu\mathchar"0\hexnumber@\symAMSb 6E}}
\makeatother
\global\let\leadsto\rightsquigarrow
\begin{document}
This is what text normally looks like: 3, third, \nicefrac{2}{3}.
\begin{exampletext}
I want my example text to look like this, but more handwritten: 3, third, $\frac{17}{25}$. Notice that even in math mode, there are no serifs.
\[
\mathbf{B}(P)=\frac{\mu_0}{4\pi}\int\frac{\mathbf{I}\times\hat{r}'}{r'^2}dl = \frac{\mu_0}{4\pi}\,I\!\int\frac{d\boldsymbol{l}\times\hat{r}'}{r'^2}% from the LaTeX Font Catalogue example
\]
\end{exampletext}
\end{document}

I wouldn't recommend changing the maths font set up only for the specialist environment because you'll end up with symbols which don't look quite the same representing the same thing depending on whether you are within the environment's scope or not. But then, I probably wouldn't use these settings anyway.
Or you could adapt Mico's method although it is a bit more complex here as lxfonts.sty changes fonts at the end of the preamble so we have to override that:
\documentclass[12pt,letterpaper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsfonts,mathtools,nicefrac,lxfonts}
\usepackage{xcolor}
\definecolor{examplecolor}{gray}{0.4}
\newenvironment{exampletext}{%
\renewcommand{\rmdefault}{llcmss}%
\renewcommand{\ttdefault}{llcmtt}%
\renewcommand{\sfdefault}{llcmss}%
\noindent\large\color{examplecolor}%
}{%
\renewcommand{\rmdefault}{lmr}%
\renewcommand{\ttdefault}{lmtt}%
\renewcommand{\sfdefault}{lmss}%
}
\AtEndPreamble{%
\renewcommand{\rmdefault}{lmr}%
\renewcommand{\ttdefault}{lmtt}%
\renewcommand{\sfdefault}{lmss}%
\renewcommand{\familydefault}{\rmdefault}%
}
\begin{document}
This is what text normally looks like: 3, third, \nicefrac{2}{3}.
\textsf{hi} \texttt{bye}
\begin{exampletext}
I want my example text to look like this, but more handwritten: 3, third, $\frac{17}{25}$. Notice that even in math mode, there are no serifs.
\[
\mathbf{B}(P)=\frac{\mu_0}{4\pi}\int\frac{\mathbf{I}\times\hat{r}'}{r'^2}dl = \frac{\mu_0}{4\pi}\,I\!\int\frac{d\boldsymbol{l}\times\hat{r}'}{r'^2}
\]
\end{exampletext}
Here is some more standard text.
\end{document}
