Understanding the associations among the data items of a given dataset plays a significant role in data mining. One of the well-known methods that deliver the associations among data items is Formal Concept Analysis (FCA) that is able to represent the associations among data items as a lattice. FCA generates a context for a given data set, then builds the associations among data items (concepts) from the context. If a decision maker changes the granularity of data, the process of creating a new lattice is repeated from the beginning. Because association mining deals with a high volume of data, the creation of a new lattice for every change in granularity of data is so computationally expensive that it is prohibitive. This lack of flexibility toward change in data granularity is a major bottleneck that limits the application of FCA in data mining. This paper suggests a solution for this observed bottleneck based on the manipulation of the existing lattice representing the associations among data items rather than building a new lattice for each iteration. The proposed solution focuses on creating a lattice for the coarser data granularity by using the lattice generated for the finer data granularity of the data in the same dataset.