Lateral intraparietal (LIP) neurons encode a vast array of sensory and cognitive variables. Recently, we proposed that the flexibility of feature representations in LIP reflect the bottom-up integration of sensory signals, modulated by feature-based attention (FBA), from upstream feature-selective cortical neurons. Moreover, LIP activity is also strongly modulated by the position of space-based attention (SBA). However, the mechanisms by which SBA and FBA interact to facilitate the representation of task-relevant spatial and non-spatial features in LIP remain unclear. We recorded from LIP neurons during performance of a task that required monkeys to detect specific conjunctions of color, motion direction, and stimulus position. Here we show that FBA and SBA potentiate each other’s effect in a manner consistent with attention gating the flow of visual information along the cortical visual pathway. Our results suggest that linear bottom-up integrative mechanisms allow LIP neurons to emphasize task-relevant spatial and non-spatial features.