How to theme Logintoboggan Access Denied Login Page
Assuming Drupal 7, if you are trying to override LT's toboggan/denied page, eg, what overall structure you see when you land on www.example.com/toboggan/denied, you could copy your theme's page.tpl.php to page--toboggan--denied.tpl.php and modify whatever you wanted in there. (If Drupal 6, the new name would be page-toboggan-denied.tpl.php.)

If you are instead (or also) trying to override the output of LT's theme function that produces the You are not authorized to access this page message on that page, you could create a function in your theme's template.php file:

function YOUR_THEME_lt_access_denied($variables) {
  return t("Whoa, Dude!  You aren't allowed in here!");
}


that would override LT's theme_lt_access_denied() function, which is just a quick:

function theme_lt_access_denied($variables) {
  return t('You are not authorized to access this page.');
} 


Or, you could instead create a template file called lt-access-denied.tpl.php in your theme that would accomplish the same thing with some potentially more fanciness:

&lt;?php 
  // contents of lt-access-denied.tpl.php
?&gt;
&lt;div class="tsk-tsk"&gt;
  Whoa, Dude!  You aren't allowed in here!
&lt;/div&gt;


In any case, if you are trying to override any of the other theme functions in LT, or any other module for that matter, you would first look in the module and search for the hook_theme() to see what's available, and in LT, that would be the logintoboggan_theme() function found in the logintoboggan.module file.  Another great resource is Drupal 7 Template (Theme Hook) Suggestions which details the template names and variants used in Drupal core modules.