  We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of
Markovian dissipation, with a focus on late-time dynamics and the approach to
thermal equilibrium. Making use of a vectorized bosonic representation of the
corresponding Lindblad master equation, we use degenerate perturbation theory
in the weak-dissipation limit to analytically obtain the eigenvalues and
eigenvectors of the Liouvillian superoperator, which in turn give access to
closed-form analytical expressions for the time evolution of the density
operator and observables. Our approach is valid for large systems, but takes
into account leading-order finite-size corrections to the infinite-system
result. As an application, we show that the dissipative Lipkin-Meshkov-Glick
model equilibrates by passing through a continuum of thermal states with damped
oscillations superimposed, until finally reaching an equilibrium state with a
temperature that in general differs from the bath temperature. We discuss
limitations of our analytic techniques by comparing to exact numerical results.
