I think there are some common public misconceptions like the nose pinching which are hard to get out of people’s heads. So I assume if you want to portrait them realistically then you have to spend more time of the show than producers would be willing to permit ;p
But of course there’s nothing preventing us from doing at least little steps at a time. So I’m considering that when answering your question: “How would I portray lucid dreaming in media?“
First of all, I think it’s a solid assumption that incubation and all that stuff that goes on in a lucid dreamer’s life before the lucid dream are not as important as the dream itself or the aftereffects, from storytelling point of view I mean. So I would forego trying to get any of that across.
As for the dream itself, I tink inception did a pretty good job at depicting a cineatistically interesting dreamworld that is also pretty close to the real thing in many aspects, so my idea of a dreamworld depiction is something like that. It must have fantastic and surreal elements and a bunch of instability and randomness. Adding different grades of perception would also be a good idea, e.g. blurring the vision in the periphery or in some specific spots, but also have some scenes that are spectacularly clear and vivid. Especially after attaining lucidity such a trick could be useful to really mark a change in the behavior of the dreamworld.
The most challenging for more would be the dreamer. I’ve recently mentioned in another topic that I don’t have much of an ego in a dream, so I would rely mostly on other dreamers’ stories to get some ideas. One thing you could do is changing body (e.g. gender, growing hair out, growing fantastic body parts…) but keep one thing like the face or the voice to bring across that it’s still the same person.
Dream characters are also an interesting thing to include. Give them erratic behavior on one hand side but make them follow their real life inspirations at other times.
I also mentioned aftereffects earlier. In a story that is not revolving around dreams only (and I think you hardly talked about those in the initial scope for this topic?), just having an instance of a lucid dream all by itself is not going to do much. I think it’s more interesting for the audience to ponder on and linger their thoughts on for some more time if it is embedded in the overall story. It should have consequences of some sort.
For example the dreamer could tell others about the dream. In this case i would use it to make some public advertisement for lucid dreaming, by having him say something like, “I had the strangest kind of dream, I could control everything. It was majestic. If only I could have them more often…“
There are other possibilities to weave it into the rest of the show/book/whatever. Use it as a precognition incident if that’s your thing. Or have the character learn something really profound that they had always been missing, most likely something about themself, but could also be something related to the story, for example how to tackle a certain problem that was a roadblock until now.
Tl;dr: Make sure to have a nice dreamworld which is easy with visual media, have the character do at least one lucid dreamy thing, and make sure it fits into the overall composition instead of being a standalone element.