This article presents the first measurement of the ratio of branching fractions B(Λ0b→Λ+cμ−νμ)/B(Λ0b→Λ+cπ−). Measurements in two control samples using the same technique B(B0→D+μ−νμ)/B(B0→D+π−) and B(B0→D∗(2010)+μ−νμ)/B(B0→D∗(2010)+π−) are also reported. The analysis uses data from an integrated luminosity of approximately 172  pb−1 of pp collisions at s√=1.96  TeV, collected with the CDF II detector at the Fermilab Tevatron. The relative branching fractions are measured to be B(Λ0b→Λ+cμ−νμ)B(Λ0b→Λ+cπ−)=16.6±3.0(stat)±1.0(syst)+2.6−3.4(PDG)±0.3(EBR), B(B0→D+μ−νμ)B(B0→D+π−)=9.9±1.0(stat)±0.6(syst)±0.4(PDG)±0.5(EBR), and B(B0→D∗(2010)+μ−ν¯μ)B(B0→D∗(2010)+π−)=16.5±2.3(stat)±0.6(syst)±0.5(PDG)±0.8(EBR). The uncertainties are from statistics (stat), internal systematics (syst), world averages of measurements published by the Particle Data Group or subsidiary measurements in this analysis (PDG), and unmeasured branching fractions estimated from theory (EBR), respectively. This article also presents measurements of the branching fractions of four new Λ0b semileptonic decays: Λ0b→Λc(2595)+μ−νμ, Λ0b→Λc(2625)+μ−νμ, Λ0b→Σc(2455)0π+μ−νμ, and Λ0b→Σc(2455)++π−μ−νμ, relative to the branching fraction of the Λ0b→Λ+cμ−νμ decay. Finally, the transverse-momentum distribution of Λ0b baryons produced in pp collisions is measured and found to be significantly different from that of B0 mesons, which results in a modification in the production cross-section ratio σΛ0b/σB0 with respect to the CDF I measurement.