Ugh, this situation blows.
What sucks is, since you met through a mutual friend, she can't just flat out reject you 'cause it might get back to said friend. But you have to really, REALLY read the wording in her statement:
"I'm sorry I missed your call yesterday." - So, she knows you called, but responds back via email? That means she got your call, heard your message, and didn't feel it was urgent enough to call you back. Very telling...
"I really appreciated you taking the time to have lunch with me on Saturday." - But she didn't say "I had such a great time," which is what most girls say when bringing up previous dates. Again, very telling...
"I actually have plans on Friday..." - But didn't give specifics to what the plans were? Saying she "has plans" is a generalization statement that she knows she can throw out there without being questioned about it. Plus, you hit her up on Tuesday - most people don't really have plans set up for Friday until about Wednesday or Thursday... but even if she DID already have plans...
"...but hopefully we'll be able to meet up some other time." - Hopefully?? As if the stars must somehow align in order for you two to get together again? She didn't give you an alternative date that WOULD work. Why? 'Cause she's not really trying to make future plans with you!
Unfortunately, sometimes the male ego will not allow us to accept this info right away, and thus needs further proof before moving on. My suggestion: wait a week, then call her up again. Don't invite her to a concert (if she said "no" to dinner, why take her to an even MORE expensive event??); instead, ask her to do something simple, like bowling or miniature golf. If she replies with "Oh, I'd love to go," then you've got a date; if she replies with "oh, I'd love to go, but I've already got plans... hope we can plan something another time though," throw the number away and move on to the next!