  For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized
Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term
afterwards is the sum of the $k$ preceding terms. In this paper, we find all
the integers that appear in different generalized Lucas sequences; i.e., we
study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)}$ in nonnegative integers
$n,k,m,\ell$ with $k, \ell\geq 2$. The proof of our main theorem uses lower
bounds for linear forms in logarithms of algebraic numbers and a version of the
Baker-Davenport reduction method. This paper is a continuation of the earlier
work [4].
