It sounds as a very good idea, but in practice the Lytro camera has a very low resolution. In the first release camera the resolution is 11 × 11 × 380 × 380 pixels, where 11 x 11 is the resolution of the cell. Whether it is able to track the wavefront distortion and what the measurement accuracy we can get? Actually I have used only the first release camera and I know nothing about the second release (Lytro illum).
I can recommend this paper which is accompanied by software release in MatLab. I believe this software is the best solution to date to deal with Lytro camera
L.F. Rodríguez-Ramos, Y. Martína, J.J. Díaza, J. Piquerasa, J.M. Rodríguez-Ramos, The Plenoptic Camera as a wavefront sensor for the European Solar Telescope (EST), Proc. SPIE 7439, Astronomical and Space Optical Systems, 74390I