Triple-negative breast cancer (TNBC) is associated with high-grade invasive carcinoma leading to a 10% to 15% death rate in younger premenopausal women. Targeting cancerous inhibitors of protein phosphatase (CIP2A) has been a highly effective approach for exploring therapeutic drug candidates. Lapatinib, a dual tyrosine kinase inhibitor, has shown promising inhibition properties by inducing apoptosis in TNBC carcinogenesis in vivo. Despite knowledge of the 3D structure of CIP2A, no reports provide insight into CIP2A ligand binding sites. To this effect, we conducted in silico site identification guided by lapatinib binding. Four of the five sites identified were cross-validated, and the stem domain revealed more excellent ligand binding affinity. The binding affinity of lapatinib in these sites was further computed using the Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) approach. According to MM/PBSA//200 ns MD simulations, lapatinib exhibited a higher binding affinity against CIP2A in site 2 with ΔG critical values of −37.1 kcal/mol. The steadiness and tightness of lapatinib with CIP2A inside the stem domain disclosed glutamic acid-318 as the culprit amino acid with the highest electrostatic energy. These results provide clear information on the CIP2A domain capable of ligand binding and validate lapatinib as a promising CIP2A inhibitor in TNBC carcinogenesis.