Within the framework of the dinuclear system model, the production cross sections for producing the new neutron-rich Lr isotopes in the multinucleon transfer reactions with 249Bk and 254Es targets were predicted. The results show that the 124Sn+254Es reaction has the highest production cross sections, followed by the 130Te+249Bk reaction. As far as the existing experimental techniques are concerned, 130Te+249Bk is the most suitable choice. With experimental techniques developing in the future, 124Sn+254Es is preferable when the thick 254Es target can be prepared. The optimal energy for producing the new neutron-rich Lr isotopes is 1.1 times the Coulomb barrier for both reaction systems, and both reactions produced 263-265,267-269Lr isotopes. The production mechanism of Lr isotopes has been investigated in the 130Te+249Bk reaction. It is found that the production of Lr isotopes mainly originates from the contribution of quasifission. And the contribution of quasifission gradually decreases with the increase of the incident angular momentum. The final production cross sections for 263-265,267-269Lr in 130Te+249Bk reaction at Ec.m.=1.10VC are 0.22 µb, 0.13 µb, 0.15 µb, 4.45 nb, 0.62 nb, and 0.03 nb, respectively.