However, lack first designated a lack of being: what is desired is being itself. "Desire is a relation to being to lack. The lack is the lack of being properly speaking. It is not the lack of this or that, but lack of being whereby the being exists." (Seminar The Ego in Freud's Theory) In "The Direction of the Treatment and the Principles of Its Power" (Écrits) Lacan argues that desire is the metonymy of the lack of being (manque à être): the subject's lack of being is at the heart of the analytic experience and the very field in which the neurotic's passion is deployed. In "Guiding Remarks for a Convention on Feminine Sexuality" Lacan contrasts the lack of being related to desire with the lack of having (manque à avoir) which he relates to demand.
Starting in his seminar La relation d'objet, Lacan distinguishes between three kinds of lack, according to the nature of the object which is lacking. The first one is Symbolic Castration and its object related is the Imaginary Phallus; the second one is Imaginary Frustration and its object related is the Real Breast; the third kind of lack is Real Privation and its object related is the Symbolic Phallus. The three corresponding agents are the Real Father, the Symbolic Mother, and the Imaginary Father. Of these three forms of lack, castration is the most important from the perspective of the cure.
It is in "La relation d'objet" that Lacan introduces the algebraic symbol for the barred Other, and lack comes to designate the lack of the signifier in the Other. Then the relation of the subject to the lack of the signifier in the Other, designates the signifier of a lack in the Other. No matter how many signifiers one adds to the signifying chain, the chain is always incomplete, it always lack the signifier that could complete it. This missing signifier is then constitutive of the subject.