Eh, no because lucid dreaming is accessed differently: it’s when you are fully asleep and then, while still sleeping, become conscious in the dream and realise you are dreaming. It’s a different thing. You are not in touch with your physical body and usually not quite conscious enough to remember who you are or where you live or maybe what century it is. You know you’re dreaming and the rest is a crapshoot, you can also fall back into regular dreaming from here, or get woken up. It’s not easy to control.
There a really good seminar on youtube on how to learn to lucid dream posted here:
Trance state is when you stay awake and enter the Theta Gamma State, aka TGS aka Rapture aka the crossroads state.
It’s best to not use the term “lucid” for this because it’s not sleeping or dreaming and that’s confusing things, so scratch that. Yes you can get deep enough that you lose awareness and start soul traveling and then it’s very similar to lucid dreaming only with more control, but let’s not go there for now.
Here’s more on the rapture
And some discussion on crossroads state for comparison:
(Actual crossroads are also used in rituals and I see the crossroads as a dark empty place in the astral where I astral travel to meet things, not a state of being and don’t use this term for it, because it’s too easy to misunderstand - there’s no crossroads involved in the trance it’s a state of mind where you are receptive to subconscious impressions.)