Can you check the version of MSI package that is on your SFDC instance ?
If it's lower than 1.4359.2, you should consider upgrading it.
Currently we do have the latest version installed, version 1.4359.2. The reason we would like to have this available for lightning is to display this visualforce page as its own sub-tab under the contact/lead lighting app page instead of just a visualforce section on the details page of the record.
Yes, then you are correct, this is not possible. It would take that MSI is turned into a lightning component, which it is not.