I think the Martins will be invited to dinners occasionally, especially after Mr. Knightley and Emma move to Donwell in a few years. I don't think that they will be reduced to merely tea-drinking. The concept of lunch did not exist back then, so, there were no lunch invitations. The Georgian morning began after breakfast and lasted until dinner time. Morning visits were paid during this time, and the guests were usually given some light snacks to eat (Miss Bates offering them cake, Lizzy and Mrs. Gardiner being offered fruits and luncheon meats at Pemberley). (JulieW's old post linked below)