We present two-dimensional numerical simulations of tilted lamellar growth patterns during directional solidification of nonfaceted binary eutectic alloys in the presence of an anisotropy of the free energy γ of the interphase boundaries in the solid. We used a dynamic boundary-integral (BI) method. The physical parameters were those of the transparent eutectic CBr 4-C 2 Cl 6 alloy. As in Ghosh et al. [Phys. Rev. E 91, 022407 (2015)], the anisotropy of γ was described by a model function with tunable parameters. The lamellarlocking effect in the vicinity of a deep minimum of the interfacial energy was reproduced. For a weak anisotropy, the lamellar tilt angle θ t was shown to depend on the growth conditions. We systematically studied the influence of usual control parameters (pulling velocity, temperature gradient, lamellar spacing, alloy concentration) on the tilted-lamellar pattern. We identified experimentally accessible conditions under which θ t falls close to the theoretical prediction based on the so-called symmetric-pattern approximation. We finally simulated locked and weakly locked lamellar patterns and found empirically a good morphological matching with experimental observations during directional solidification of thin CBr 4-C 2 Cl 6 samples.