Galois (concept) lattice theory has been successfully applied in data mining for the resolution of the association rule problem. In particular, structural results about lattices have been used in the design of efficient procedures for mining the frequent patterns (itemsets) in transaction databases. Since such databases are often dynamic, we propose a detailed study of the incremental aspects in lattice construction to support effective procedures for incremental mining of frequent closed itemsets (FCIs). Based on a set of descriptive results about lattice substructures involved in incremental updates, the paper presents a novel algorithm for lattice construction that explores only limited parts of a lattice for updating. Two new methods for incremental FCI mining are studied: the first inherits its extensive search strategy from a classical lattice method, whereas the second applies the new lattice construction strategy to the itemset mining context. Unlike batch techniques based on FCIs, both methods avoid rebuilding the FCI family from scratch whenever new transactions are added to the database and/or when the minimal support is changed.