Lamellar eutectic alloys have two main types (floating or locked) of growth patterns depending on the orientations of the two eutectic phases. Recent theoretical studies have suggested that the existence of locked lamellar patterns is linked to that of deep minima in the surface energy plot of the interphase boundaries [Ghosh et al., Phys. Rev. E 91, 022407 (2015)]. We present an experimental study aiming at testing this prediction. We used a near-eutectic In-In2Bi alloy that solidifies into a tetragonal phase ε (In-11.5 atBi) and a hexagonal phase δ ( (In2Bi). Thin samples of this alloy were solidified using a rotating directional solidification stage and analyzed for crystallographic texture by X-ray diffraction. A series of samples with low (1 to 3°) mosaic spreads were found to contain either of the following coincidence relationships: A = {2¯1¯10}δ // {111}^ɛ or E = {1¯102}^δ // {111}^ɛ. A-type eutectic grains exhibited a locked type of growth, and E-type eutectic grains a floating type of growth. Given that according to standard crystallographic criteria A-type interphase boundaries have a much smaller surface energy than E-type ones, these findings are in agreement with the theoretical predictions.