Typesetting Poetry Half-Lines in Memoir Class

There is the parcolumns package that you might want to look at (texdoc parcolumns) but this will set the left and right half-lines in two columns which is not what you appear to want. I think that the simplest is to use \hspace but perhaps abbreviated as you will need somehow to distinguish between the two halves of a line.

\newcommand*{\hld}{\hspace{3em}} % change 3em to suit

and then

\begin{verse}
First left half \hld first right half \\
Second left half \hld second right half \\
% and so on
\end{verse} 

I'll go ahead and post the solution I ended up using.

\newcommand{\halfline}{\leavevmode\unskip\quad\ignorespaces}

The commands \leavemode and \unskip are there at the beginning to gobble up the extra spaces before the command, so I can typeset my poems more naturally, without having to worry about accidentally producing extra space. For example,

\begin{verse}
First left half \halfline first right half \\
Second left half \halfline second right half \\
\end{verse} 

would produce precisely the same output as:

\begin{verse}
First left half{\halfline}first right half \\
Second left half{\halfline}second right half \\
\end{verse} 

The problem is where the break line spacer should be. Without a clear rule in terms of text width, number of words or characters, or verse syntax, it must be placed manually. Assuming that (otherwise clarify your question, please), the space seem close to a double quadrat (2em) that is a standard horizontal spacer in LaTeX, so simply write \qquad where you consider that it should be:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lettrine}
\usepackage{imfellEnglish}
\usepackage{graphicx}
\begin{document}
\lettrine[lines=3]{\resizebox{.3em}{.75em}H}{wæt}. 
wē Gār-Dena\qquad in gēar-dagum\\
 þēodcyninga\qquad þrym gefrūnon,\\
hū ðā æþelingas\qquad ellen fremedon.
\end{document}