So here's what I don't connect with on the bolded above.
There are two appointment times available as of the time the OP calls the student. Now, in the meantime, anything can happen, including one or both of those appointment times no longer being available due to being booked by someone else. Or is it the understanding that once those two times are offered to someone via voice mail, they must remain open indefinitely till that person calls in or shows up for one of them or the hour passes with Lisa not seeing anyone?
If another student were to need an appointment, is the OP now obligated to say that 8:30 to 9:30 are not available because they have been offered to another student who may or may not use them, and they must remain open until that student responds or until that time passes, unused?
Or is the implication that OP must subsequently call the student back if/when either or both of the appointments get booked by other people? Potentially three calls: 1) offer the two times 2) sorry one of them has been reserved 3) sorry the other one's been reserved.
That just doesn't ring right with me. It's unfortunate that the student wasn't able to confirm the appointment by closing time regardless of the reason. But until the student confirms her intent to take one of those times and the OP confirms that the time the student wants is still available, I'd say that the appointment is not set in stone.
(I'm not quoting myself just to preserve space)
If the times are offered, I think it is reasonable to assume that the interviewer is indeed holding those times. If they aren't, they shouldn't offer the specific times. It's very easy to just say "we have time slots available Wednesday morning, so call to schedule one of them." That is a much more specific (and therefore more clear) message. Even better is "We have time slots available Wednesday morning, so please call by 4:30 p.m. today to schedule one of them." That communicates both that there is availability, what the general timeframe is, and what the deadline for scheduling is.
Scheduling interviews is a large portion of what I do at work all day, and I will say that if I'm trying to juggle candidates or other schedules or whatever, I don't commit to any time, with anyone, until I'm sure it will work. I call the person we want to interview and ask them when they are available, and I don't give them a time slot until I'm ready to give it to them firmly. I contact the people who will be conducting the interview to find out their availability, and if it's limited or time is short, I also ask them to hold it open for me. It is only at that point that I even identify specific times that can work for interviews, and I don't leave time slots in a voicemail message unless I'm at that point, know I have space available, and am pretty sure it's going to work.
Using the method where I basically don't tell anyone anything until I've got a full schedule put together allows me to schedule interviews with very little notice successfully, but it does take more effort and time on my part to do it that way. That is the tradeoff with scheduling in general, and scheduling interviews in particular: you can either have it be easy, or you can have it happen quickly. You can rarely have both.
So if you're going to offer specific times, then yes, you do have to hold them for at least a reasonable length of time to give the person a chance to either confirm one of them or decline both. "Reasonable length of time" varies depending upon the situation, but I don't think it can ever be less than 24 hours. Even the most interested, engaged, and capable candidates have other things going on in their lives that sometimes prevent them from checking email or answering the phone. And if the person scheduling interviews is not able, for whatever reason, to listen to voicemail or check email (or make calls) outside of the 8-5 business day, you have to expect it's going to take longer. A lot of people simply are not available between 8 and 5. The earlier in a person's career you are, the more likely that is to be true (since entry level jobs tend to be the most restrictive about taking time away from your desk and/or engaging in personal business while at your desk).