Does Sartre's bad faith point to the same structure Lacan missed in fantasy?

Sartre argued that bad faith is consciousness fleeing from its own freedom by pretending to be a fixed thing, and I think this reveals something Lacan got backwards about the fundamental fantasy. The standard Lacanian reading treats fantasy as the subject's construction of a scenario to approach some lost fusional wholeness (the objet a as stand-in for pre-symbolic completeness). If you follow Sartre's insight that consciousness is already relational and free, the deeper fantasy is the ego's construction of itself as a bounded, separate entity. The fundamental fantasy is isolation, not fusion. Separation is the thing consciousness has to build and maintain through constant effort (bad faith, in Sartre's terms), because the default condition of consciousness is openness to the world and to others. Heidegger's Mitsein points the same direction: being-with is structurally prior to being-alone, so solitary selfhood is the constructed achievement. This inversion reframes the direction of psychoanalytic treatment and aligns it with the existentialist claim that authenticity means confronting your freedom and relationality as opposed to your separateness.