We study the space of Lie algebras equipped with left-invariant complex structures, \( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \) , with particular attention to their degenerations and deformations. To this end, we identify certain invariants that remain well-behaved under degenerations while preserving the complex structure. These concepts are then applied to the four-dimensional case. Additionally, we explore applications to the study of left-invariant Hermitian structures on Lie groups, and we discuss some aspects of the deformation theory within \( \mathcal {L}_{ J_{\tiny {\text{ cn }}} }(\mathbb {R}^{2n}) \) .
