There are many algorithms developed for improvement the time of mining frequent itemsets (FI) or frequent closed itemsets (FCI). However, the algorithms which deal with the time of generating association rules were not put in deep research. In reality, in case of a database containing many FI/FCI (from ten thousands up to millions), the time of generating association rules is much larger than that of mining FI/FCI. Therefore, this paper presents an application of frequent closed itemsets lattice (FCIL) for mining minimal non-redundant association rules (MNAR) to reduce a lot of time for generating rules. Firstly, we use CHARM-L for building FCIL. After that, based on FCIL, an algorithm for fast generating MNAR will be proposed. Experimental results show that the proposed algorithm is much faster than frequent itemsets lattice-based algorithm in the mining time.