If you're using one of the standard document classes, you can merely add the following to your LaTeX preamble:
\makeatletter
\newcommand{\versefont}{}
\renewenvironment{verse}
{\let\\\@centercr
\list{}{\itemsep \z@
\itemindent -1.5em%
\listparindent\itemindent
\rightmargin \leftmargin
\advance\leftmargin 1.5em}%
\item\relax\versefont}
{\endlist}
\makeatother
This will allow you to redefine \versefont to make your font selections in the preamble, or through the body text using an ERT.
If you're using the verse package, then your preamble should look like this in order to do the same:
\usepackage{verse}
\makeatletter
\newcommand{\versefont}{}
\renewenvironment{verse}[1][\linewidth]{
\stepcounter{verse@envctr}%
\setcounter{poemline}{0}\refstepcounter{poemline}%
\setcounter{vslineno}{1}%
\let\\=\@vscentercr
\list{}{\itemsep \z@
\itemindent -\vindent%
\listparindent\itemindent
\parsep \stanzaskip
\ifdim #1 < \linewidth
\rightmargin \z@
\setlength{\leftmargin}{\linewidth}%
\addtolength{\leftmargin}{-#1}%
\addtolength{\leftmargin}{-0.5\leftmargin}%
\else
\rightmargin \leftmargin
\fi
\addtolength{\leftmargin}{\vindent}%
\versefont}
\item[]}{\endlist}
\makeatother
The above code just grabbed the verse environment definition from verse.dtx and inserted \versefont (defined to be empty).
\versefontbefore\listin both cases, so that it can contain also font size changing commands. – egreg Feb 05 '13 at 07:58