We present a laboratory analysis of the use of a 19-core photonic lantern (PL) in combination with neural network (NN) algorithms as an efficient focal plane wavefront sensor (FP-WFS) for adaptive optics (AO), measuring wavefront errors (WFE) such as low wind effect (LWE), Zernike modes, and Kolmogorov phase maps. The aberrated wavefronts were experimentally simulated using a spatial light modulator with combinations of different phase maps in both the approximately linear regime (average incident RMS WFE of 0.88 rad) and in the nonlinear regime (average incident RMS WFE of 1.5 rad). Results were analyzed using an NN to determine the transfer function of the relationship between the incident WFE at the input modes at the multimode input of the PL and the intensity distribution output at the multicore fiber outputs end of the PL. The root mean square error (RMSE) of the reconstruction of petal and LWE modes were just 2.87×10−2 rad and 2.07×10−1 rad respectively, in the nonlinear regime. The reconstruction RMSE for Zernike combinations ranged from 5.67×10−2 rad to 8.43×10−1 rad, depending on the number of Zernike terms and incident RMS WFE employed. These results demonstrate the promising potential of PLs as an innovative FP-WFS in conjunction with NNs.