<div class="panel">
<?php $homethumb = get_post_meta($post->ID,'homethumb', true);?>
<a href="<?php the_permalink() ?>" title="<?php the_title(); ?>" > <img src="<?php bloginfo('url'); ?>/wp-content/uploads/<? echo strtolower($homethumb); ?>.jpg" width="200" height="120" alt="<?php the_title(); ?>"/> </a>
</div>

Discover using short open tags, then it wouldn't work, since your echo statement utilizes a <? (as opposed to a <?php) tag.

The next fixes the issue:

<div class="panel">
<?php $homethumb = get_post_meta($post->ID,'homethumb', true);?>
<a href="<?php the_permalink() ?>" title="<?php the_title(); ?>" > <img src="<?php bloginfo('url'); ?>/wp-content/uploads/<?php echo strtolower($homethumb); ?>.jpg" width="200" height="120" alt="<?php the_title(); ?>"/> </a>
</div>