First of all headphones will be wireless. Bluetooth will be the standard connection for listening to music. Cables will only be used for charging or if the battery runs low. A lightning connected pair of headphones will always need a DAC and an amplifier. With all this electronics in the headphones it's no big deal to add a small battery and a blutooth circuit.
In consequence the headphones will not have a fixed cable anymore and I don't believe there will be any lightning port in the headphones. In my opinion the headphones will provide an usb-c port. So you can connect them with any standard usb-c cable to any usb-c port for charging and/or listening. To connect them with the lightning port on iPhone you will use a standard lightning-to-usb-c cable that can also be used to connect with the new macbooks and charge the iPhone form a usb-c charger. The current lightning-to-usb cable and usb-charger will simply be replaced with usb-c versions as usb will be completely replaced with usb-c on any device.
Agreed headphones will not have fixed cable anymore. That's already starting to become the norm with 3.5mm headphones, and BT headphones.
But, not all headphones will be wireless. In the short term that's going to be a lot more expensive. There's going to be a quality gap as well. And in the long term, there are always going to be people who won't be comfortable using wireless products next to their heads, and no matter how good the battery a need to plug in the headset. Some people just aren't going to be interested in a product they have to remember to keep charged.
Headphones may eventually use USB-C ports for connectivity, but in Apple's world, Beats may use Lightning, or offer both USB-C and Lightning so that Apple customers can daisy chain their headphones and share a connection, just as they do now, and still be compatible with Android and PCs. Flip the included USB-C to Lightning cable around and it works on an Android letting other Android users daisy chain. If it's wireless, then both Apple and Android customers can tap into it.
The New MacBooks will almost certainly have Lightning ports which will give Apple customers the ability to plug in Lightning equipped headphones natively, as well as charge them, and also charge the MacBook with the same cable used on the iPhone (while leaving all the USB-C ports free). And depending on what's coming with the iPhone via smart connector charging, and likely eventually wireless charging, the headphones can be charged in the iPhone just like the Apple Pencil can be charged in the iPad. And look at the Apple Pencil solution to charging without the iPad -- a double ended female Lightning adapter. I'd expect to see something similar used on the headphones.
For most manufacturers, USB-C ports on the headphones likely make the most sense, but I'll bet initially there will be a lot of proprietary headphone connectors, and Lightning is fine as far as that goes. If the point is to make sure someone who uses Lightning headphones doesn't get caught out without the ability to charge the headphones, or use them when the battery runs out, then I'd wager that for the next couple of years, such a person is going to have a better chance of finding a Lightning cable than a USB-C cable anyway, as well as a compatible USB-A charger or laptop to plug it into.