The observed enhancement of the Fe Kα line in three gravitationally lensed QSOs (MG J0414+0534, QSO 2237+0305, and H1413+117) is interpreted in terms of microlensing, even when equivalent X-ray continuum amplification is not observed. In order to interpret these observations, first we studied the effects of microlensing on quasar spectra produced by a straight fold caustic crossing over a standard relativistic accretion disk. The disk emission was analyzed using the ray-tracing method, considering Schwarzschild and Kerr metrics. When the emission is separated into two regions (an inner disk corresponding to the Fe Kα line and an outer annulus corresponding to the continuum, or vice versa), we find microlensing events that enhance the Fe Kα line without noticeable amplification of the X-ray continuum, but only during a limited time interval. Continuum amplification is expected if a complete microlensing event is monitored. Second, we studied a more realistic case of amplification by a caustic magnification pattern. In this case we could satisfactorily explain the observations if the Fe Kα line is emitted from the innermost part of the accretion disk while the continuum is emitted from a larger region. We also studied the chromatic effects of microlensing, finding that the radial distribution of temperature in the accretion disk, combined with microlensing itself, can induce wavelength-dependent variability of ~30% for microlenses with very small masses. All these results show that X-ray monitoring of gravitational lenses is a method well suited for studying the innermost structure of active galactic nucleus accretion disks.