We study the metrical theory of the growth rate of digits in Lüroth expansions. More precisely, for x ∈ (0, 1], let [d1(x), d2(x), …] denote the Lüroth expansion of x. We completely determine the Hausdorff dimension of the sets \(\matrix{{{E_{\sup }}(\psi ) = \Big\{ x \in (0,1]:\mathop {\lim \sup }\limits_{n \to \infty } {{\log {d_n}(x)} \over {\psi (n)}} = 1\Big\} ,} \cr {E(\psi ) = \Big\{ x \in (0,1]:\mathop {\lim }\limits_{n \to \infty } {{\log {d_n}(x)} \over {\psi (n)}} = 1\Big\}}}\) and \({E_{\inf }}(\psi ) = \Big\{ x \in (0,1]:\mathop {\lim \inf }\limits_{n \to \infty } {{\log {d_n}(x)} \over {\psi (n)}} = 1\Big\},\) where ψ: ℕ → ℝ+ is an arbitrary function satisfying ψ(n) → ∞ as n → ∞.
