Using a proton-proton collision data sample corresponding to an integrated luminosity of 3 fb(-1) collected by LHCb at center-of-mass energies of 7 and 8 TeV, about 3800 Ξ(b)(0) → Ξ(c)(+)π(-), Ξ(c)(+)) → pK(-)π(+) signal decays are reconstructed. From this sample, the first measurement of the Ξ(b)(0) baryon lifetime is made, relative to that of the Λ(b)(0) baryon. The mass differences M(Ξ(b)(0))-M(Λ(b)(0)) and M(Ξ(c)(+))-M(Λ(c)(+)) are also measured with precision more than 4 times better than the current world averages. The resulting values are τ(Ξ(b)(0))/τ(Λ)(b)(0)) = 1.006 ± 0.018 ± 0.010,M(Ξ(b)(0))-M(Λ(b)(0)) = 172.44 ± 0.39 ± 0.17 MeV/c(2),M(Ξ(c)(+))-M(Λ(c)(+)) = 181.51 ± 0.14 ± 0.10 MeV/c(2),where the first uncertainty is statistical and the second is systematic. The relative rate of Ξ(b)(0) to Λ(b)(0) baryon production is measured to be f(Ξ)(b)(0))/f(Λ)(b)(0))B(Ξ(b)(0) → Ξ(c)(+)π(-))/B(Λ(b)(0) → Λ(c)(+)π(-))B(Ξ(c)(+) → pK(-)π(+))/B(Λ(c)(+) → pK(-)}π(+)) = (1.88 ± 0.04 ± 0.03) × 10(-2),where the first factor is the ratio of fragmentation fractions, b → Ξ(b)(0) relative to b → Λ(b)(0). Relative production rates as functions of transverse momentum and pseudorapidity are also presented.