Two-dimensional coherent electronic spectroscopy (2DES) is a powerful technique in distinguishing homogeneous and inhomogeneous broadening contributions to the spectral line shapes of molecular transitions induced by environment fluctuations. Using an excitonic model of a double-ring LH2 aggregate, we perform simulations of its 2DES spectra and find that the model of a harmonic environment cannot provide a consistent set of parameters for two temperatures: 77 K and room temperature. This indicates the highly anharmonic nature of protein fluctuations for the pigments of the B850 ring. However, the fluctuations of B800 ring pigments can be assumed as harmonic in this temperature range.