Using data collected by the CLEO III detector at CESR, we report on the first observation of the decays Lambda(c)(+)-->Lambdapi(+)pi(+)pi(-)pi(0) and Lambda(c)(+)-->Lambdaomegapi(+). The branching fractions are measured relative to the pK(-)pi(+) mode; we find B(Lambda(c)(+)-->Lambdapi(+)pi(+)pi(-)pi(0))/B(Lambda(c)(+)-->pK(-)pi(+))=0.36+/-0.09(stat)+/-0.09(syst) and B(Lambda(c)(+)-->Lambdaomegapi(+))/B(Lambda(c)(+)-->pK(-)pi(+))=0.24+/-0.06(stat)+/-0.06(syst). We also observe a small excess of events in Lambda(c)(+)-->Lambdaetapi(+), eta-->pi(+)pi(-)pi(0) from which we find B(Lambda(c)(+)-->Lambdaetapi(+))/B(Lambda(c)(+)-->pK(-)pi(+))=0.41+/-0.17+/-0.10 with a corresponding limit of <0.65% at 90% confidence level. This rate is consistent with previous measurements of Lambda(c)(+)-->Lambdaetapi(+), eta-->gammagamma. We find that the combined branching fractions for Lambda(c)(+)-->Lambdaomegapi(+) and Lambda(c)(+)-->Lambdaetapi(+) comprise (87+/-13)% of the total Lambda(c)(+)-->Lambdapi(+)pi(+)pi(-)pi(0) rate. We set an upper limit on B(Lambda(c)(+)-->Lambdapi(+)pi(+)pi(-)pi(0))/B(Lambda(c)(+)-->pK(-)pi(+)) for non-omega and non-eta modes of 0.13 at 90% confidence level.
