If you look at the code for \makeletterclosing in the file moderncvstyleclassic.sty you will see the following:
\renewcommand*{\makeletterclosing}{
\@closing\\[3em]%
{\bfseries \@firstname~\@familyname}%
\ifthenelse{\isundefined{\@enclosure}}{}{%
\\%
\vfill%
{\color{color2}\itshape\enclname: \@enclosure}}}
There's a line break after \@closing with a vertical spacing of 3em, this causes the page break.
Add this to your document preamble, all I did is git rid of the forced line break.
\makeatletter
\renewcommand*{\makeletterclosing}{
\@closing%\\[3em]%
{\bfseries \@firstname~\@familyname}%
\ifthenelse{\isundefined{\@enclosure}}{}{%
\\%
\vfill%
{\color{color2}\itshape\enclname: \@enclosure}}}
\makeatother
A blank page doesn't appear if you used just two paragraphs of lipsum, i.e \lipsum[1-2]. So it's all about margins. Obviously, you don't want to delete the line break if you're going to insert a firstname and familyname since they will be in the same line as the closing.