The expected usage of BC2N graphene-like monolayer as a drug delivery system for the β-lapachone anticancer drug is analyzed by using periodic DFT computations. The best possible direction for the interaction of β-lapachone with BC2N nanosheet is resolved and adsorption energies are determined. In the most stable complexes, the drug interacts with the desired monolayer with an adsorption energy of the −1.81 eV. Because of the way that pH around cancerous cells is lower than normal cells, drug release around the cancerous cells upon protonation was researched. The extent of the determined solvation energy reveals the solubility of the proposed drug-carrier system in the aqueous medium enveloping the human organs. The consequences of the current examination affirmed the ability of a BC2N monolayer as a drug delivery vehicle for β-lapachone to treat cancer.