In a recent paper we studied the effect of new-physics operators with different Lorentz structures on the semileptonic Λb → Λcτν¯τ decay. This decay is of interest in light of the R(D(∗)) puzzle in the semileptonic B¯ → D(∗)τν¯τ decays. In this work we add tensor operators to extend our previous results and consider both model-independent new physics (NP) and specific classes of models proposed to address the R(D(∗)) puzzle. We show that a measurement of R(Λc) = B[Λb → Λcτν¯τ ]/B[Λb → Λcℓν¯ℓ] can strongly constrain the NP parameters of models discussed for the R(D(∗)) puzzle. We use form factors from lattice QCD to calculate all Λb → Λcτν¯τ observables. The Λb → Λc tensor form factors had not previously been determined in lattice QCD, and we present new lattice results for these form factors here.