Atmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un-resolved and under-resolved GWs have to be represented using a sub-grid scale (SGS) parameterization in general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely-used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high-fidelity data (e.g., GW-resolving simulations). However, this is a non-trivial task, and the quality of the ML-based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (GWD) from high-resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high-resolution ($\Delta x =3~km$) simulations using weather research and forecasting model (WRF). Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large-scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale-awareness in the development of data-driven parameterizations.