Energy filtered CBED patterns of the Cr-stabilized L1(2) phase of a titanium tri-aluminide alloy reveal deficit higher order Laue zone (HOLZ) lines in the zeroth order diffraction disk, for which the expected 4-mm symmetry is significantly broken in the <001> projection. This apparent break of symmetry may be explained by the presence of lattice strains of order 10(-3). Effects of strain-induced lattice distortions on HOLZ line symmetries are calculated by an introduction of rhombohedral, tetragonal or monoclinic distortions to the cubic unit cell. It is shown how tensile and shear components of strain affect the overall HOLZ line symmetries in different ways.