This paper presents an iterative and interactive information retrieval system for Web search using Formal Concept Analysis (FCA). FCA provides a natural way to organize objects according to their properties and it has been used in recent work to organise search engine results. The navigation over the lattice helps the user to explore a structured and synthetic result. Such a lattice contains concepts that are relevant and others that are not relevant regarding a given information retrieval task. In this way, lattices are introduced in 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. The lattice is dynamically updated for a better fit to the request.