We argue that the quality of a summary can be evaluated based on how many concepts in the original document(s) that can be preserved after summarization. Here, a concept refers to an abstract or concrete entity or its action often expressed by diverse terms in text. Summary generation can thus be considered as an optimization problem of selecting a set of sentences with minimal answer loss. In this paper, we propose a document concept lattice that indexes the hierarchy of local topics tied to a set of frequent concepts and the corresponding sentences containing these topics. The local topics will specify the promising sub-spaces related to the selected concepts and sentences. Based on this lattice, the summary is an optimized selection of a set of distinct and salient local topics that lead to maximal coverage of concepts with the given number of sentences. Our summarizer based on the concept lattice has demonstrated competitive performance in Document Understanding Conference 2005 and 2006 evaluations as well as follow-on tests.