Should I charge entry for a public lecture?
I doubt exclusivity as represented by an entrance fee would attract people to a lecture. After al, it is the subject that is of importance. thus the advertisement is key and the way you set your topic in a wider perspective. If the topic concern people such as climate change, environmental issues, medicine to mention a few, people will come. It will be more difficult to attract people to topics they either do not know anything about or are not interested in (or in the worst case, is not widely reported in media). Thus, my negative perspective is that the success of attracting an audience is to a large extent a question of how the topic is known by and an interest of the public.

So, I would advice against charging for the lecture and put all efforts into making the lecture as interesting as possible for the intended audience. And, to do this by coupling the topic to a larger picture that is relevant to the public. And finally, if you do not get a huge audience, it does not mean there is anything wrong with your research or lecture, public interest varies over time and research can have huge relevance for important aspects of society and life without attracting a wide audience.