For any x∈(0,1), let x=[d1(x),d2(x),⋯,dn(x)] be its Lüroth expansion. Denote the maximal digits of the first n digits by Ln(x)=max{d1(x),⋯,dn(x)}. For any real number 0<α<β<∞, we determine the Hausdorff dimension of the exceptional set
Fϕ(α,β)={x∈(0,1):lim infn→∞Ln(x)ϕ(n)=α,lim supn→∞Ln(x)ϕ(n)=β},
where ϕ(n)=nγ(γ>0) or enγ(γ>0). This supplements the results of [13]. Similarly, the corresponding exceptional sets of the sums of digits in Lüroth expansion are also studied.