The adsorption of boron and oxygen atoms onto mono- and multi-layer graphene leads to the formation of a buckled graphene layer (BO-graphane) and a 2D diamond-like structure (BO-diamane) sandwiched between boron monoxide layers per DFT calculations. BO-graphane has a calculated Young's modulus (E) of 750 GPa and BO-diamane 771 GPa, higher than the calculated E of -F, -OH, and -H diamanes; this is due to the presence of B-O bonds in the functionalizing layers. Electronic band structure calculations show BO-graphane and BO-diamane are wide band gap semiconductors with an indirect band gap up to a thickness of three layers (3L). Phonon dispersion and ab - initio molecular dynamics (AIMD) simulations confirm dynamic and thermal stability, maintaining structural integrity at 1000 K. The room-temperature lattice thermal conductivity of BOgraphane and BO-diamane is found to be 879 Wm-1K-1 and 1260 Wm-1K-1, respectively, surpassing BeO (385 Wm-1K-1), MgO (64 Wm-1K-1), and Al2O3 (36 Wm-1K-1); and F-diamane (377 Wm-1K-1), and comparable to H-diamane (1145-1960 Wm-1K-1), suggesting them as candidates for thermal management in applications.