Inertial microfluidic devices (IMDs) are a low-cost and high-throughput means of manipulating, separating, and focusing suspended particles on the micrometer scale. The precise nature of the lift force affecting particle motion within IMDs is difficult to determine analytically. As a result, designing these inertial microfluidic devices typically requires either financially costly physical design cycles or computationally costly direct numerical simulation. Existing data-driven attempts at alleviating these costs require the impractical step of generating a new model for every new channel cross-sectional geometry. Herein, we re-formulate traditional expressions for lift force to be completely independent of channel geometry and then use this geometry-free re-formulation to parameterize a fully-connected neural network (FCNN). We train this FCNN on a publicly available lift force dataset for rectangular channels and show that with our parameterization the FCNN is able to generalize to triangular, semicircular, and trapezoidal channel geometries. We suggest possible ways to improve the generalizability of the model --- mostly centered around increasing training data heterogeneity --- with the hope that our model will eventually be integrated into computational fluid dynamics software to drastically reduce the computational burden of simulating IMDs.