In this work, we implement closed-shell Brueckner orbitals for the efficient domain-based local pair natural orbital DLPNO-CCSD(T) and DLPNO-CCSD(T)_Λ methods of the free and open-source Psi4 package. We introduce a new algorithm that allows Brueckner orbitals to be computed within the DLPNO framework, resulting in the novel DLPNO-BCCD(T) and DLPNO-BCCD(T)_(Λ₂) methods. We show that DLPNO-BCCD(T) approximates its canonical BCCD(T) counterpart with significantly lower errors relative to the errors incurred by DLPNO-CCSD(T) over CCSD(T). Through a test on the S22 set of noncovalent dimers, the peak error across the set is reduced from 0.36 kcal mol⁻¹ to 0.25 kcal mol⁻¹ using normal cutoffs, and 0.28 kcal mol⁻¹ to 0.13 kcal mol⁻¹ at tight cutoffs. In addition, we show that BCCD(T)_(Λ₂), a Λ₂-only implementation of Brueckner orbitals for the asymmetric triples method, generally produces the best agreement with CCSDT, compared to the (T), (T)_Λ, and B(T) perturbative triples corrections. This is established through benchmarks on thermochemistry tests on the barrier heights of semibullvalene and bullvalene Cope rearrangement, while the robustness of DLPNO-BCCD(T)_(Λ₂) is demonstrated along bond-breaking potential energy curves, where it matches the orbital-optimized quasi-variational asymmetric renormalized-triples OQVCCDAR(T) method closely for single-bond breaking, and approximates DLPNO-CCSDT respectably even when triple bonds are stretched, at a fraction of the computational cost.