Yes and no.
I’m running the T6 Pro using their relatively newly rebranded Residio app. I’m not an add-on developer but I spent a good deal of time getting OH to communicate through their cloud REST API with limited success. As best as I can tell their authenticate is broken and sometimes it just forgets about the refresh token it gave you but won’t let you get a new auth token. You can see my attempts at Honeywell Home API with openHAB using just rules.
Once authenticated it worked well though, until the access token timed out. Then it was 50/50 whether it could successfully get a new one or not.
I’m assuming the T6 Lyric doesn’t use the evohome API for which there is an add-on.
Over the years I’ve searched GitHub for some python scripts or node programs that might bridge between the two and work better, but for the most part my thermostat is set and forget, especially post COVID where it’s rare that our home is not occupied by at least one family member. I have limited integration with OH through the Amazon Control Binding and full control through Google Assistant so if we ever need to change the target temp or mode we usually just do so through a Google Home or Hub device (I’ve only one Echo device given to me free when Amazon disabled the ability of my printer to order toner when it was low automatically without it. All it does is show me ads, order toner, and let OH see and control my thermostat and outdoor lighting).