  In this paper we apply the nested algebraic Bethe ansatz to compute the
eigenvalues and the Bethe equations of the transfer matrix of the new
integrable Lindbladian found in [1]. We show that it can be written as an
integrable spin chain consisting of two interacting XXZ spin chains. We
numerically compute the Liouville gap and its dependence on the parameters in
the system such as scaling with the system length and interaction strength.
