Adding a class to last post in the_date

Its possible, you can get the next post date to compare using get_adjacent_post function

change your code to this:

<?php while ( have_posts() ) : the_post(); 

//hold current date
$curent_date = $post->post_date;
//fix the format to YYYY-MM-DD
$curent_date = substr($curent_date,0,strpos($curent_date," "));
$next_post = get_adjacent_post(false,'',false) ;
if (!$next_post == ''){
    //get next post's date
    $next_date = $next_post->post_date;
    //fix the format to YYYY-MM-DD
    $next_date = substr($next_date,0,strpos($next_date," "));
    if ($next_date != $curent_date){//last post of the date
        the_date('l jS F Y','<h2 class="lats-of-date>','</h2>');
    }
}else{
 the_date('l jS F Y','<h2>','</h2>'); 
}
?>
<hr />   
<div class="post">                  
    <h3><a href="https://wordpress.stackexchange.com/questions/13280/<?php the_permalink(); ?>" title="<?php printf( esc_attr__( 'Permalink to %s', 'twentyten' ), the_title_attribute( 'echo=0' ) ); ?>" rel="bookmark"><?php the_title(); ?></a></h3>                                     
    <?php the_excerpt(); ?>             
</div> <?php endwhile; ?> <hr class="btm" />

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