Firstly, well done for making such an effort to be grandparents in common to DD's child. These regular Sunday Lunches keep the communication channels open and allow your DD to process the change in her family structure. I also applaud bringing along friends - as sort of UN peacekeepers to ensure that occasion didn't degenerate into regrettable behaviour event. Much more comfortable for all the adults present.
However bringing a sexual partner along does the opposite of depressurising a potentially fraught meeting. It adds to the difficulty.
I feel that there is the opportunity to agree a rule of "no romantic partners". It just isn't appropriate, and do you want your DGC to meet a succession of GD's lady friends?
When my DD left her partner and moved on with embarrassing haste, we refused to meet her new partner, even though he was living with our DGC, because in our house we have a 3 month rule. New partners are not introduced to parents until the relationship is of 3 months duration. We found this rule to be a real lifesaver.
I don't see why you have to put your DD and DGC through the painful experience of witnessing an encounter with your ex under such demanding circumstances. I would be clear with my DD that the romantic interest should be uninvited. If that's too embarrassing, your DD needs to eat 2 dinners, one with her Dad and one with you. The dinners need'nt be on the same day.
I'd make the rules clear, a family meal with non romantic interest friends along to keep things civilised whilst you are working through this difficult time, or separate gettogethers.
Good luck