Should I charge entry for a public lecture? I am a research scientist, and as part of my role I am expected to perform some form of public outreach and engagement. I enjoy outreach activities and giving public lectures. 

I have a suspicion that free public lectures are usually poorly attended. I suspect that the attitude is one of "Well, it's free and you get what you pay for". Certainly the quality of artistic performances that I've seen is strongly correlated with entrance fee. 

While it is a reasonable expectation that my Faculty would pay for the costs of lecture room hire, advertising, possibly even tea and biscuits, I wonder if there is an advantage of charging a nominal fee to attend, to overcome the low-quality perception of a free 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.