Examples of dBH-LC formation through SN or inner binary merger in triple evolution are shown. Both panels display the evolution of component mass, radius, orbital separation, and eccentricity as functions of time. In both panels, the gray region indicates the phase when the inner binary undergoes RLOF, and the red region marks the dBH-LC phase. In addition, the initial parameters of the two triples shown in the figure are as follows: In the left panel, the masses of the system are m₁ = 23.57 M_⊙, m₂ = 14.96 M_⊙, and m₃ = 0.13 M_⊙. The semi-major axes and eccentricities are a_in = 1902.10 R_⊙, a_out = 19130.05 R_⊙, e_in = 0.51, and e_out = 0.46. The inclinations and arguments of pericenter are cos i_in = 0.80, cos i_out = 0.04, ω_in = 6.00, and ω_out = 0.07. In the right panel, the masses of the triple are m₁ = 52.84 M_⊙, m₂ = 8.07 M_⊙, and m₃ = 9.00 M_⊙. The semi-major axes and eccentricities are a_in = 66.26 R_⊙, a_out = 2666.19 R_⊙, e_in = 0.18, and e_out = 0.66. The inclinations and arguments of pericenter are cos i_in = −0.98, cos i_out = −0.99, ω_in = 0.79, and ω_out = 2.99.