We report the discovery of Xi(c)(3055)(0), observed by its decay into the final-state Lambda D-0, and present the first observation and evidence of the decays of Xi(c)(3055)(+) and Xi(c)(3080)(+) into Lambda D+. We also perform a combined analysis of the Lambda D+ with the Sigma K-++(c)- and Sigma(c)*K-++(-) decay modes to measure the ratios of branching fractions, masses and widths with improved accuracy. We measure the ratios of branching fractions B(Xi(c)(3055)(+) -> Lambda D+)/B(Xi(c)(3055)(+) -> Sigma(++)(c) K-) = 5.09 +/- 1.01 +/- 0.76, B(Xi(c)(3080)(+) -> Lambda D+)/B(Xi(c)(3080)(+) -> Sigma K-++(c)-) = 1.29 +/- 0.30 +/- 0.15, and B(Xi(c)(3080)(+) -> Sigma(c)*K-++(-))/B(Xi(c)(3080)(+) -> Sigma K-++(c)-) = 1.07 +/- 0.27 +/- 0.04, where the uncertainties are statistical and systematic. The analysis is performed using a 980 fb(-1) data sample collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.