Decision-making can be significantly enhanced by knowledge extraction techniques such as Formal Concept Analysis (FCA), which provides a structured way to analyze and organize data. However, in distributed environments, information is often fragmented, arriving in streams rather than as a complete dataset. Consulting the entire dataset at once is not always feasible due to time and resource constraints. While an existing batch algorithm allows concept lattice computation without requiring full attribute knowledge, batch processing is inherently unsuitable for dynamic, continuously evolving data. In this article, we propose an incremental algorithm for concept lattice computation in arbitrarily distributed formal contexts, which can efficiently update the lattice as new information becomes available. Our method ensures that knowledge extraction remains computationally feasible even when data is incomplete, distributed, or evolving over time. We further analyze the complexity of our approach in comparison to the existing batch-based distributed algorithm, highlighting its advantages in stream processing scenarios. By addressing the limitations of batch computation and enabling real-time lattice updates, our work contributes to enhancing FCA’s applicability in distributed and dynamic knowledge systems. The proposed incremental approach paves the way for more adaptive, efficient, and scalable knowledge extraction methods, particularly in fields requiring real-time decision-making and pattern discovery.