  Monitored quantum system have sparked great interest in recent years due to
the possibility of observing measurement-induced phase transitions (MIPTs) in
the full-counting statistics of the quantum trajectories associated with
different measurement outcomes. Here, we investigate the dynamics of the
Lipkin-Meshkov-Glick model, composed of $N$ all-to-all interacting spins $1/2$,
under a weak external monitoring. We derive a set of semiclassical stochastic
equations describing the evolution of the expectation values of global spin
observables, which become exact in the thermodynamic limit. Our results shows
that the limit $N\to\infty$ does not commute with the long-time limit: while
for any finite $N$ the esamble average over the noise is expected to converge
towards a trivial steady state, in the thermodynamic limit a MIPT appears. The
transition is not affected by post-selection issues, as it is already visible
at the level of ensemble averages, thus paving the way for experimental
observations. We derive a quantitative theoretical picture explaining the
nature of the transition within our semiclassical picture, finding an excellent
agreement with the numerics.
