Lepton Flavour Universality tests with semileptonic Λb → Λ c * decays are important to corroborate the present anomalies in the similar ratios RD(∗), and can provide complementary constraints on possible origins of these anomalies beyond the Standard Model. In this paper we provide — for the first time — all the necessary theoretical ingredients to perform and interpret measurements of RΛ∗c at the LHCb experiment. For this, we revisit the heavy-quark expansion of the relevant hadronic matrix elements, and provide their expressions to order αs and 1/m accuracy. Moreover, we study the sensitivity to the form factor parameters given the projected size and purity of upcoming and future LHCb datasets of Λb→Λ∗cμν¯¯¯ decays. We demonstrate explicitly the need to perform a simultaneous fit to both Λ c * final states. Finally, we provide projections for the uncertainty of RΛ∗c based on the form factors analysis from semimuonic decays and theoretical relations based on the heavy-quark expansion.