Taking X-ray/UV/optical observations of local Seyfert nuclei into account, we look for evidence supporting a reverberation scenario in three bright gravitationally lensed quasars at 1 < z < 2. The analysis is based on the normalized structure function of luminosities at middle UV wavelengths (observer-frame optical bands). We concentrate on tackling two issues: initial logarithmic slope and achromaticity. Due to the presence of significant observational noise in the g - band magnitudes of SBS 0909+532, we cannot prove the achromaticity of the structure function of this double quasar. However, the r -band records of SBS 0909+532 leads to a steep initial growth of the corresponding structure function, which is basically consistent with the traces of reverberation in local Seyfert nuclei (initial slope β ~ 0.7). The structure function of Q0957+561 is roughly achromatic. Moreover, its initial slope agrees with a β = 0.7 law. Apart from the structure function analysis, there are complementary observations in favour of a reverberation scenario in Q0957+561. The third object is Q2237+0305. The light curves of its four images incorporate both intrinsic and extrinsic (microlensing) variability, and we are not able to fairly determine an initial intrinsic slope for this quadruple quasar. Finally, we present some ongoing projects to better understand the mechanism of intrinsic variability (rest-frame timescales below 100 d) in gravitationally lensed quasars at (z)~ 1.5.