Through this proposal, we want to study the magnetic excitations in a very rare realization of a frustrated two-leg ladder system Li2O(CuSO4)2 using inelastic neutron scattering. This compound displays an intriguing phase transition under the form of a weak and progressive distortion of the high-temperature tetragonal crystal at about 140 K, possibly driven by magnetic frustration. State-of-the-art density functional calculations reveal that this structural distortion is accompanied by a strong magnetic dimerization. Our main purpose is to assess the validity of this scenario by probing the temperature-dependent magnetic excitations in the compound: (i) through a measure of the evolution of the spin gap with the temperature across the phase transition and (ii) in the dimerized phase, through the extraction of the characteristic intradimer distance via constant energy transfer scan in wave vector Q. The experimental results will be confronted to other results obtained recently in infra-red spectroscopy and interpreted using exact diagonalization calculations.