A Cox Process $X_t$ is, in a nutshell, a Poisson process whose intensity $\lambda_t$ is a stochastic process itself. If $\lambda_t$ is independent from $X_t$ and it's possible to sample, then one can simulate $X_t$ generating first a trajectory $\lambda^0_t$ of $\lambda_t$ and then simulate a non-homogeneous Poisson process with intensity $\lambda^0_t$ (see here for example, page 3) by thinning.
My question is: how can one simulate $X_t$ if $\lambda_t$ depends on $X_t$ (and so we cannot sample $\lambda_t$)?