I was recently given two free tickets to an art exhibition. I invited two longstanding and very good friends and said we would split the cost of the one extra ticket between the three of us. My friends were adamant that they'd pay half each of the cost of the additional ticket. I don't know why - I thought I was lucky to have the two free tickets so I was quite happy to pay for only one third of a ticket.
That is different from your scenario because this lady is asking someone that you don't know. It wouldn't be the money that would bother me (though I can see that some people might think it a bit cheeky), but the fact that I didn't know the person and might not feel that comfortable. On that level, I think it is perhaps discourteous of your friend.
However, if it were me and the person concerned was a good friend of mine, I think I would go along with it as I wouldn't want something relatively minor like this to risk spoiling the friendship. If she did something similar again, I would be less accommodating.
If it really rankles with you, it is probably best to be honest and say, as you haven't had the opportunity to get to know the other person, you would prefer only the two of you to have lunch.