Is it reasonable for a guest lecturer/class speaker to ask for a stipend?

I would look at this from the perspective of the professor inviting you. Most of the people a university invites to speak are professors (or postdocs/ phd students) from other universities. For these, giving the talk is beneficial career wise so there is no additional speakers fee. But they have to travel to the university, very often from out of town. This means there is no easily available budget for paying you to speak but there usually is a budget for your travel expense. Usually this also covers inviting you for a meal.

So I would recommend asking for travel expenses. They should definitely pay for your parking ticket and if you come by car there is probably some fuel money or something like that as well. If you are interested the professor will probably also offer to take you out for dinner afterwards. This should be easy from their perspective. Asking to be paid for the talk as such could be a lot more complicated. If you want that to make it worth your while be prepared that the answer might be no.

Yes it is reasonable to ask for some form of compensation. It could be monetary or some privilage or networking benefits or even a nice dinner invite (as Jon mentioned). As professional ettiquitte, the professor should have asked you about compensation or at least asked about your comfort level. This should have been done for the very first lecture.

Asking now is awkward, but you can still ask tactfully. There's no shame in doing so. I'm quite sure the professor can easily request the administration to either waive your parking fee or pay it on your behalf. You are a guest.

Also learn the art of saying "no". I recently said no to a neighbour who asked if I could give a talk at her kid's school. I asked if I'd be paid for it. She said "no", and I just said that if there's no payment, I'd not be interested. There were no hard feelings afterward. It's understandable if someone does not want to spend time and money for free and get nothing in return. Moreover, I've noticed that people who don't value others time and money tend to take you for granted.

Some years ago, as a senior employee of a public sector body with no teaching or 'outreach' responsibilities, I accepted an invitation to "give a talk" at a business school. It turned out that I was expected to run a two-hour session for the MBA class.

No fee was offered. At that time any fee would have gone to my employer so I had no particular incentive to chase the school for a few pounds, and my employer, quite uninterested in any fees I might earn, would have thought that there was a benefit in influencing some MBA students that my organisation had such brilliant teachers as me... or if the students did not think I was brilliant, then the loss to the organisation would be minimal.

But if I were asked to do give a talk, now that I am no longer employed by such an organisation, I would go straight to the point " Are you offering a fee?". Then make the decision on the basis of the answer to that question.