Thank you for your post and welcome to the Bose Community.
This is not possible as the Lifestyle system can only input Bluetooth audio and not output. However, you can connect your QC 35 Headphones via the interconnect cable into the headphone port on the front of the Control Console if you wish to do so.
If you have any further questions, please do get back to us.
chnically you could as the Lifestyle has a headphone out by 3.5mm. But it will depends on the adapter and what you are doing. If you are outputting music it shouldn't be an issue. If you are outputting sound for video you will probably experience a lag in the sound. Some adapters are better than others, but most will lag
I visited the Bose showroom in the mall of Emirates, Dubai. The manager of the showroom said we don't have any option to get Bluetooth out from lifestyle 600! period.
I was very disappointed with the answer!
It wouldn't be a Bose solution, it would be a third party transmitter taht would send from the LIfestyle. And because it won't give you the experience Bose would want you to have, it's unlikely they would recommend doing it.