For the most part, Roman women had a greater degree of independence than Greek women, and were allowed to travel to the market and even the games without necessarily having a male escort. Often, slaves accompanied Roman women, both to carry her wares and as a display of wealth. And restrictions varied in severity from household to household as well, given that Roman men possessed much broader authority to regulate or not regulate their wives' movement than in Greece, where the law often came into play more strongly.

That said, the primary role of the Roman woman was to be the manager of the household, first and foremost, and protect and advance her husband's interests. If she were to have a lunch date with her girlfriends, it would likely be similar to the meetings that her husband was having. Women were expected to cultivate useful relationships with their husband's business partner's wives and act as go-betweens for their husbands and their birth families. Most marriages were dynastic and political in nature, at least in the upper classes.

Of course, we don't have much to go on from Roman women. The only female sources I can think of off the top of my head are (coincidentally) both poets named Sulpicia. Therefore, anything about Roman women is an argument from silence and an exploration of their roles through the male lens.

Roman women do not seem to have held the same social functions as Roman men, but the Bona Dea feast is a prominent example of Roman women holding and organizing their own event. Bona Dea is notable, if only because Roman men actually had no idea what went on behind closed doors, since no men were allowed inside, except for one notable example. In 63 BC, Clodius Pulcher, a controversial Roman politician and opponent of Cicero, purportedly infiltrated the festival disguised as a female flute player, causing a massive scandal that resulted in Caesar divorcing his wife, who had hosted the feast.

Did Roman women have female friends? Yes. Did they gossip? Absolutely (probably less than Cicero, but he's a bit overactive). They did eat lunch together but also had to notify their husbands before hand (at least when the husbands were at home). They could host friends or have feasts but almost always under the watchful eyes of their husbands or fathers.