Apple just revealed iPhone 7 which comes with earbuds with lightning connector. Will these earbuds work with other iPhones with lightning connector such as iPhone 6/6s?
Yes. According to Apple's product site for the lightning adapter:
This adapter lets you connect devices that use a 3.5 mm audio plug to your Lightning devices.
What’s in the Box
Lightning to 3.5 mm Headphone Jack Adapter
Works with all devices that have a Lightning connector and support iOS 10 or later, including iPod touch, iPad, and iPhone.
Yes, it will. several high end headphones already use the lightning connector rather than the 3.5 mm headphone jack. http://www.pocket-lint.com/news/136466-best-lightning-headphones-2016-phones-for-iphones