I would probably just say, "I've been happy to cover you in the past, but you have never payed me back, and I just don't have the funds available to cover you today." I could just bring $20 cash and claim I forgot my purse too, luckily I had $20 in the car. I could go further and say, "This lunch is not a mystery, you need to be better about remembering your purse. What would you do if you needed gas?" I can understand this need to keep up with the Jones' and not appear to be cheap or stingy. I also question continuing friendships with the group if judgement is passed on not being rich enough.
To move onto a new bent, these people could be living outside their means, projecting riches, including the car, but are knee deep in dept and are, in reality, broke. That's not to say the LW or anyone else in the group should feel obligated to cover this woman's meals and expenses. She should not be attending if she can't afford to eat out. Just say no.