We're working with an OpenCTI adapter that the vendor has open-sourced for us. So we have the ability to customize the dialer page which is by design written in Visualforce. The dialer appears in the Lightning app's Utility Bar. We are trying to make the incoming call process in Lightning Experience (not console) as friendly as possible.
What we'd really love to see happen is, when an incoming call comes in, a second component (built in Lightning) pops up from the Utility Bar. If there's any way we can throw an event that would be received by a Lightning Component that would be great, as we've already proven we can respond to the event by having the Lightning utility pop itself open.
However it seems that the mode in which the OpenCTI dialer page loads does not have access to any methods that can throw application-level Lightning events in Lightning Experience (sforce.one is unavailable, the undocumented SfdcApp is unavailable). The available OpenCTI
screenPop method for Lightning Experience covers use cases such as navigation, new record modal, search, but nothing that actually integrates into Lightning's event model to allow us to throw an event without leaving the page the user is currently on.