Ferroelastic LaAlO3 (space group R3¯c) exists with two different microstructures: twins and tweed. Both microstructures contain electrical dipole moments. Polarity inside ferroelastic twin walls has been shown using two complementary experimental techniques and identical samples. PFM reveals a weak piezoelectric effect at the loci of the domain walls. In tweed samples, the PFM signal is finite but variable in the entire sample. PFM shows that same characteristic tweed microstructure as observed optically. The piezoelectric effect is of a similar magnitude inside twin walls and, space averaged, in the tweed microstructure (and approximately one order of magnitude smaller than in c-oriented PbTiO3 single crystals). Resonance piezoelectric spectroscopy proves that domain walls vibrate under the application of an external driving electric field. The resonance frequency is very close to stress induced vibrations. This is evidence for weak but finite coupling between the local dipole moments in the domain walls and the external electric field. The same coupling and the piezoelectric response are much stronger in the tweed sample. Symmetry breaking by dipolar vectors in a LaAlO3 sample with tweed has been confirmed by the observation of optical second harmonic signals. The noncentrosymmetric point group is identified as 3m in agreement with earlier work on twinned LaAlO3 but in contradiction with predictions of Landau-Ginzburg theory of simple ferroelastic wall structures.