The \(LU\) factorization of a \(k\)-lower Hessenberg Toeplitz matrix \(H_{n}^{(k)} (a,b,c)= [h_{i,j}]_{1\leq i,j \leq n}\) with entries \(h_{i,i}=a\), \(h_{i,i+1}=b\), \(h_{i+k,i}=c\) and zero otherwise is deduced. Indeed, the explicit expression of the matrices \(L\) and \(U\) is obtained as well as their inverses. As a direct consequence, the authors obtain the inverse of \(H_{n}^{(k)} (a,b,c)\).