This is just my .02 based on my own experience. But I tried occasional dinners/cookouts with my wayward H (at my S8's request). And it did more damage than good. It prevented me from detaching and it raised my expectations. It also allowed my H to cake-eat. All that being said, he was still actively in an A. Do you have any way to verify your W has definitely ended her A?
I mean, I could see lunch as a way for you to show a new side of you. But to begin trying to piece things together when your W hasn't asked you what it would take to work on your M, hasn't given you full access to her phone (transparency) or hasn't involved you in sending (hopefully X)OM a NC letter seems like putting the cart before the horse to me.
Am I missing something? If she has given you her usernames/passwords and access to her phone, then you can "trust ... but verify" and act accordingly.
M: 40 H: 44 Married 14 years S11 & D6; D20 & D19 from previous M 2BDs/PAs, 8 years apart Piecing: April 2014