The LHCb experiment has explored lepton universality violation in $b \to c \ell^- \overline{\nu}_{\ell}$ and $b \to s \ell^+ \ell^-$ transitions through the measurement of the ratios $R(D^*)$ and $R_K$. These ratios are found to be compatible with the Standard Model expectation at the level of 2.1$\sigma$ and 2.6$\sigma$, respectively. Additionally, searches for lepton flavour violation in $B$, $D$ and $\tau$ decays have been performed. No signal for such decays is found, and upper limits on their branching fractions are set.