I am not allowed to share admin credentials for that site.
Couldn't you have a look at the file /.. domain ../plugins/system/t4/src/t4/Document/Template.php?
You changed this in 2.0.6 and added code to support the different edit modes of the template.
The error is thrown at line 30.
Thanks!
Frank
Edit: When I change lines 30 and 31 of Template.php to
/* $this->t4EditLayout = $this->doc->params->get('system_t4frontendedit',0);*/
$this->t4EditLayout = 0;
the error disappears. I know this is not clean at all but could probably give you a hint.