We report the results of several studies of the Lambda(c)(+)pi(+)pi(-)X final state in continuum e(+)e(-) annihilation data collected by the Belle detector. An analysis of angular distributions in Lambda(c)(2880)(+)-->Sigma(c)(2455)(0,++)pi(+,-) decays strongly favors a Lambda(c)(2880)(+) spin assignment of 5/2 over 3/2 or 1/2. We find evidence for Lambda(c)(2880)(+)-->Sigma(c)(2520)(0,++)pi(+,-) decay and measure the ratio of Lambda(c)(2880)(+) partial widths Gamma(Sigma(c)(2520)pi)/Gamma(Sigma(c)(2455)pi)=0.225+/-0.062+/-0.025. This value favors the Lambda(c)(2880)(+) spin-parity assignment of 5/2(+) over 5/2(-). We also report the first observation of Lambda(c)(2940)(+)-->Sigma(c)(2455)(0,++)pi(+,-) decay and measure Lambda(c)(2880)(+) and Lambda(c)(2940)(+) mass and width parameters. These studies are based on a 553 fb(-1) data sample collected at or near the Upsilon(4S) resonance at the KEKB collider.