As an expert non-native speaker, I can sense a slight difference in the two expressions, in that "being unselfconscious" can be used in a positive sense, whereas "lacking self-consciousness" is definitely negative.
Is that so also for native speakers?
I generally agree with TaliesinMerlin's comment. When applied to a person (rather than say a text), "lacking self-consciousness" suggests not having the capacity for it, which may well be a negative, since self-consciousness is often a desirable trait. e.g. "Steven completely lacked self-consciousness at the party and ended up really upsetting Guilia".
"Being unselfconscious" is more of a temporary state, and I generally hear it as a more positive thing: e.g. "When speaking in public, being unselfconscious is often helpful." Negation with "not" rather than "un-" might be more natural in some cases: "Guilia really put Sam at ease, so he was not self conscious when he had to perform.". Note also the meaning "without affectation or pretence" at https://www.wordreference.com/definition/unselfconscious : this is generally positive.
The negative sense in "lacking self-consciousness" perhaps comes from "lacking", which often points up something that might be desirable. In any case, I generally understand it in the sense of second meaning at https://www.wordreference.com/definition/self-consciousness : "conscious[ness] of oneself or one's own being.", which is a often positive, unless forthright, confident or brazen behaviour is desired!
In short, I don't think they're completely synonymous, but the meanings are close.
