I've never read Lacan and judging by what I've heard of his prose I doubt I ever will.
Having said that here is how someone at Hawaii university characterises Lacan's idea of the Mirror Stage in personal development.
The idea of the "mirror stage" is an important early component in Lacan’s critical reinterpretation of the work of Freud. Drawing on work in physiology and animal psychology, Lacan proposes that human infants pass through a stage in which an external image of the body (reflected in a mirror, or represented to the infant through the mother or primary caregiver) produces a psychic response that gives rise to the mental representation of an "I". The infant identifies with the image, which serves as a gestalt of the infant's emerging perceptions of selfhood, but because the image of a unified body does not correspond with the underdeveloped infant's physical vulnerability and weakness, this imago is established as an Ideal-I toward which the subject will perpetually strive throughout his or her life.
For Lacan, the mirror stage establishes the ego as fundamentally dependent upon external objects, on an other. As the so-called "individual" matures and enters into social relations through language, this "other" will be elaborated within social and linguistic frameworks that will give each subject's personality (and his or her neuroses and other psychic disturbances) its particular characteristics.
If this explanation is accurate then sure, you're correct. Correct in that the Lacanian notion of the subject does indeed appear to be relational.
But a small note, I would not characterise Descartes' notion of the subject as atomic, instead I would say reflexive, self reflecting as you say. I see what you are trying to get at with atomic -- meaning unitary, indivisible, individual, self-contained, not reliant on another. But may I suggest that reflexivity works better?
And yes, it would seem correct to position the Lacanian subject in opposition to the Cartesian one but wouldn't you say that Lacan gives us a psychological explanation whereas Descartes gives us a more philosophical one?