In the traditional SLAM framework, the state estimate is updated at a fixed frequency. However, such an approach can be inefficient because there is no need to update the state estimate when the deviation between two sequential estimates is within the predefined tolerance bound. Thus, an adaptive scheme for frequency updating seems more promising from the point view of computational efficiency. Inspired by the concept of Lebesgue sampling, a new SLAM framework (or LS-SLAM) is proposed, in which the updating frequency is determined in an adaptive manner according to the motion of robot. When the updating frequency of LS-SLAM is inconsistent with the sampling frequency of observational signals, constraints are introduced to synchronize the state estimate updating instants with the observational sampling instants. The experimental results for an open source dataset show that the introduction of Lebesgue sampling into SLAM can improve the computational efficiency of the algorithm without sacrificing accuracy.