Three tests of lepton flavour universality in semitauonic B decays using LHCb Run 1 data are presented. Namely, these are measurements of the ratios of branching fractions of B0->D* (tau/mu) nu (using both muonic and 3-prong hadronic tau decays) and Bc->J/psi (tau/mu) nu (using the muonic tau decay). All three results, along with similar measurements from BaBar and Belle, lie above the Standard Model prediction, hinting at the violation of lepton flavour universality. Prospects for future improvements in precision are also discussed.