In LCRM Release 12.36, the ability to create a contact was changed from an S Control to a standard Visualforce page.  This visualforce page is not compatible with custom Account record types.  Our Best Practices documentation advises against creating custom contact or account types, as certain functionalities within LCRM cannot be guaranteed to be compatible with these custom record types, including the updated contact create visualforce page.  

While we would not recommend the continued use of custom account types, you may be able to first create a new contact from the Contact tab, and then associate the new contact with the custom account.