Sparse-LiDAR-prompted depth foundation models (PromptDA, Prior Depth Anything, DMD3C) have shown strong results on indoor scenes or within KITTI's standard 80-meter evaluation cap. However, two limitations remain: (i) systematic distance-stratified evaluation in long-range driving regimes (50-150 m) is largely absent; (ii) prior approaches built on disparity-based foundations rely on pre-interpolated dense priors, leaving truly sparse LiDAR injection on point-map foundations (e.g., MoGe-2, NeurIPS 2025) unexplored. We present SLIM (Sparse-LiDAR Injected Monocular geometry), the first adaptation of MoGe-2 to accept truly sparse LiDAR input. SLIM integrates a partial-convolution sparse encoder with a multi-scale fusion neck that fuses LiDAR features into the point-map decoder at five scales. We adopt density-agnostic training (random injection ratio in [0.005, 0.30]) so a single model serves diverse input densities. On Virtual KITTI and CARLA, SLIM reduces the absolute relative error of the MoGe-2 baseline by approximately 39-51% at 100-150 m. Ablation across six injection ratios shows partial-convolution injection improves both AbsRel and RMSE on Virtual KITTI in all six settings; on CARLA, AbsRel improves in five of six settings (one near-tie at 0.015 differs by 0.0013), and RMSE is comparable across encoders, with partial-convolution improving in three settings (by up to 0.31 unit) and losing by at most 0.11 unit in the other three.