The aero-engine lubrication system is vital for lubricating, protecting, and cleaning mechanical components under diverse conditions. However, long-term lubricant consumption—due to factors like pipeline damage, bearing cavity leakage, and component fatigue—can degrade system and engine performance. Accurate prediction of lubricant consumption is thus essential for proactive maintenance and improved reliability. To overcome the limitations of existing methods that rely solely on historical data and single-level feature extraction, this paper proposes a multivariate regression algorithm: Bilateral Tree Convolutional Network–Bidirectional Gated Recurrent Unit–Attention (BiTCN-BiGRU-Attention), further optimized by random forest. BiTCN captures bidirectional temporal features to enrich semantics; BiGRU enhances temporal modeling by removing directional constraints; and Attention improves prediction by refining feature weighting. Experiments show the proposed method outperforms baselines, demonstrating strong potential for integration into aero-engine health management systems.