We experimentally study the spectral lasing response of on-chip InP network random lasers under illumination of different input image shapes. Deep-learning models have become increasingly omipresent throughout society. However, they are blighted by exponentially soaring energy demands. Physical implementations of neural networks are emerging as an attractive solution for performing machine learning more energy-efficiently than conventional GPU hardware by mimicking the complex structure of biological brains. However, not many platforms which can natively receive unprocessed raw image data as light have so far been demonstrated - a highly-appealing approach which deserves attention. Here, we demonstrate an optical system with spectral response to image input. Specifically, we report on designable solid-state InP network random lasers, based on random graph networks etched into wafer-bonded InP. The networks lase over a broad wavelength range and show a plethora of modes formed by multiple scattering paths. These modes are highly sensitive to illumination patterns due to their unique and highly overlapping spatial distribution.