In 2014. BESIII collected a data sample of 567 pb-1 at Ecm = 4.6 GeV, which is just above the Lambda_c+ pair production threshold. By analyzing this data sample, we have measured the absolute branching fractions for many decays of Lambda+c for the first time. These decays include the semileptonic decays of Lambda e+v, Lambda mu+v, the hadronic decays of pKs, pK-pi+, pK-pi+pi0, Lambda pi+, Lambda pi+pi0, Sigma+pi+pi0, pKspi0, Lambda pi+pi+pi-, pKspi+pi-, Sigma0pi+, Sigma+pi0, Sigma+omega, pphi, pK+K-|non-phi, ppi+pi-, nKspi+, Sigma-pi+pi+(pi0) and inclusive decay Lambda+anything. The decays of ppi+pi-, nKspi+ and Sigma-pi+pi+pi0 are observed for the first time and the others are measured with significantly improved precision. These results are important to benifit the development of the related theories, and provide important inputs for both charmed baryons and B physics.