This dataset comprises 2200 Grand Canonical Monte Carlo (GCMC) simulation runs of a binary Lennard-Jones (LJ) fluid. The simulations were performed under a variety of random external potentials. The primary purpose of this data is to serve as a training set for machine learning models aimed at deriving the c1-functional, a crucial component for classical density functional theory. This work is connected to the research detailed in the paper "Learning the bulk and interfacial physics of liquid-liquid phase separation" (to be published) and the associated SWNeural software available on GitHub (https://github.com/SilasRobitschko/SWNeural) The simulated system is a binary symmetric Lennard-Jones fluid with the following parameters: same-species interaction (ϵ11=ϵ22) and weakened cross-species interaction (ϵ12=0.7⋅ϵ11). The particle sizes are identical (σ1=σ2), and the potential is truncated at 2.5σ (without an energy shift being applied). The data was generated using the MBD software package, developed by Florian Sammüller at the University of Bayreuth (https://gitlab.uni-bayreuth.de/bt306964/mbd).