Ratios of isospin amplitudes in hadron decays are a useful probe of the interplay between weak and strong interactions and allow searches for physics beyond the standard model. We present the first results on isospin amplitudes in b-baryon decays, using data corresponding to an integrated luminosity of 8.5 fb(-1), collected with the LHCb detector in pp collisions at center of mass energies of 7, 8, and 13 TeV. The isospin amplitude ratio vertical bar A(1) (Delta(0)(b) -> J/psi(Sigma(0)) /A(0) (Delta(0)(b) -> J/psi Lambda)vertical bar, where the subscript on A indicates the final-state isospin, is measured to be less than 1/21.8 at 95% confidence level. The Cabibbo suppressed Xi(0)(b) -> J/psi Lambda decay is observed for the first time, allowing for the measurement vertical bar A(0) (Xi(0)(b) -> J/psi Lambda) / A(1/2 )(Xi(0)(b) -> J/psi Xi(0))vertical bar = 0.37 +/- 0.06 +/- 0.02, where the uncertainties are statistical and systematic, respectively.