Apples use of Lightning connector in MFi Program
There is no clause in the MFi Program's Term's and Conditions that specifically deny or allow a said accessory concept. Only demarcation Apple does is whether an accessory type is or is not part of the MFi Program.

For e.g. accessories that connect to the Lightening port are a part of MFi Program. On the other hand, accessories that only use standard Bluetooth profile or Bluetooth Low Energy, non-electronic cases etc. are not part of MFi Program.

I recommend you go through the MFi FAQ's before proceeding.

The FAQ's specifically answers some questions which may be relevant in your case. Quoting them below:


  Can you review my product concept and advise if I need to join the MFi Program?
  
  If you intend to develop an electronic accessory which will connect to iPhone, iPad or iPod using proprietary technology, your company must join the MFi Program. Apple is unable to provide feedback regarding a product concept prior to joining the MFi Program.
  
  
  
  
  Is there a program fee for participation in the MFi Program?
  
  There is no program fee at this time. However, all program applicants must purchase and complete a company identity verification through a secure, third party Web-site.