You can split the contents of an environment at every occurrence of \item which allows you to separate out the "arguments" for every list item. That way you can perform an action (conditionally) on an \item:

\documentclass{article}
% https://tex.stackexchange.com/a/127014/5764
\usepackage{xparse,environ,soul}
\ExplSyntaxOn
\NewEnviron{oddevenitemize}[1][]
{
\int_zero:N \l_odd_even
\keys_set:nn { oddeven/itemize } { #1 }
\seq_set_split:NnV \l_oddeven_itemize_input_seq { \item } \BODY
\seq_pop_left:NN \l_oddeven_itemize_input_seq \l_tmpa_tl
\tl_use:N \l_oddeven_itemize_pre_tl
\seq_set_map:NNn
\l_oddeven_itemize_output_seq
\l_oddeven_itemize_input_seq
{ \exp_not:n { \__oddeven_itemize_do:n { ##1 } } }
\seq_use:NV \l_oddeven_itemize_output_seq \l_oddeven_itemize_sep_tl
\tl_use:N \l_oddeven_itemize_post_tl
}
\seq_new:N \l_oddeven_itemize_input_seq
\seq_new:N \l_oddeven_itemize_output_seq
\cs_generate_variant:Nn \seq_set_split:Nnn { NnV }
\cs_generate_variant:Nn \seq_use:Nn { NV }
\int_new:N \l_odd_even
\keys_define:nn { oddeven/itemize }
{
pre .tl_set:N = \l_oddeven_itemize_pre_tl,
post .tl_set:N = \l_oddeven_itemize_post_tl,
sep .tl_set:N = \l_oddeven_itemize_sep_tl,
action .code:n = \cs_set_eq:NN \__oddeven_itemize_do:n #1,
action .initial:n = \use:n,
}
\NewDocumentCommand{\normalitem}{m}{%
\item #1
}
\NewDocumentCommand{\underlineodd}{m}{%
\int_incr:N \l_odd_even
\item
\int_if_odd:nTF { \l_odd_even }
{\ul{#1}}% Underline odd
{#1}% Do nothing for even
}
\NewDocumentCommand{\underlineeven}{m}{%
\int_incr:N \l_odd_even
\item
\int_if_odd:nTF { \l_odd_even }
{#1}% Do nothing for odd
{\ul{#1}}% Underline even
}
\ExplSyntaxOff
\begin{document}
\begin{oddevenitemize}[
action=\underlineodd,
pre=\begin{itemize},
post=\end{itemize},
]
\item First
\item Second
\item Third
\item Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed semper eros sed quam ullamcorper iaculis tincidunt feugiat neque.
Donec ut risus at arcu tristique porttitor. Proin sollicitudin
sollicitudin aliquam. Mauris rutrum, erat et gravida ornare, odio
justo aliquet ipsum, at venenatis sem quam fermentum tortor.
\item Integer et ante non libero scelerisque hendrerit at nec dui.
Proin ante velit, finibus id tempor id, laoreet eu quam.
Suspendisse semper ex id magna luctus egestas.
Phasellus pharetra nibh bibendum felis commodo pulvinar.
\item Last
\end{oddevenitemize}
\end{document}
The items are formatted using an action. In the above example, we use \underlineodd, but you can switch this to \underlineeven to underline even-numbered \items.
Underlining is done with support from soul to allow for line-breaks.
Reference: