This paper presents an iterative and interactive information retrieval system to search on the web using formal concept analysis (FCA). FCA provides a natural way to organize objects according to their properties and it has been used in recent works to organise in a more convenient manner answers provided by a search engine. The navigation into the lattice helps the user explore a structured and synthetic result. Such a lattice contains concepts that are relevant and some others that are not relevant for a given information retrieval task. We introduce lattices into an interactive and iterative system. The user expresses his negative or positive agreement with some concept of the lattice, in respect with his objective of information retrieval. These user choices are converted into operations over the lattice so to make the context change and to better fit user needs.