We report the results of several studies of the Λc+π+π-X final state in continuum e+e- annihilation data collected by the Belle detector. An analysis of angular distributions in Λc(2880)+→Σc(2455)0, ++π+,- decays strongly favors a Λc(2880)+ spin assignment of 52 over 32 or 12. We find evidence for Λc(2880)+→Σc(2520)0,++π+,- decay and measure the ratio of Λc(2880)+ partial widths Γ(Σc(2520)π)/Γ(Σc(2455)π)=0.225±0. 062±0.025. This value favors the Λc(2880)+ spin-parity assignment of 52+ over 52-. We also report the first observation of Λc(2940) +→Σc(2455)0,++π+,- decay and measure Λc(2880)+ and Λc(2940)+ mass and width parameters. These studies are based on a 553fb-1 data sample collected at or near the Υ(4S) resonance at the KEKB collider.