When something lapses, it ends. Many types of business offers and/or transactions are made with a specified time limit in place. Once the predetermined and announced period of time has elapsed, the offer is no longer valid or available - it has become a lapsed offer.
Examples of situations using lapsed offers include discount coupons that are good until a given date, contracts that must be signed and validated by a given date or they become null and void, or proposals to take a defined course of action that must be approved within a certain period of time or the proposal is withdrawn. The purpose of a lapsing offer is to limit the amount of time for which the company or business is responsible for honoring the terms of the offer.