A signed total double Roman k-dominating function (STDRkDF) on an isolated-free graph G = (V, E) is a function f : V (G) → {-1, 1, 2, 3} such that (i) every vertex v with f(v) = -1 has at least two neighbors assigned 2 under f or at least one neighbor w with f(w) = 3, (ii) every vertex v with f(v) = 1 has at least one neighbor w with f(w) ≥ 2 and (iii) ∑_u∈N(v) f(u) ≥ k holds for any vertex v. The weight of an STDRkDF is the value f(V (G)) = ∑_{u∈V (G)} f(u). The signed total double Roman k-domination number γ_stdR ^k (G) is the minimum weight among all signed total double Roman k-dominating functions on G. In this paper we present sharp lower bounds for γ_stdR ² (G) and γ_stdR ³ (G) in terms of the order and the size of the graph G.