routes.php

<?php

Route::post('authenticate', function() {
  // This gets userHash and decrypts it to an ID
  // try{} catch(xxxException $e) {} - if its not correct format (script kiddies) it will throw an exception of some kind
  $user_id = Crypt::decrypt($request->input('userHash'));
  // Authenticate
  Auth::loginUsingID($user_id);
  // redirect anywhere you want
  return redirect('/');
});

SteamController.php

In this file where you log-in. You need to do these things:

1. Get steamID64 and find the user_id
2. Encrypt the user_id
3. Either make Route::post(authenticate) to a get so you can redirect without problems or you make it to GET and with parameters (less safe)
3.1 http://stackoverflow.com/questions/5576619/php-redirect-with-post-data
3.2 You will also need to think of a way to prevent "hackers"
3.2.1 Maybe csrf_token will help?
3.3 Don't use redirect('authenticate') because then it will use the same domain, instead use redirect('http://correctdomain.com/authenticate')
4. Should work
5. Profit?