What happens in the distant future of the universe? In the standard cosmological model LCDM the universe approaches the asymtotic deSitter state in the distant future. Is it correct to say that all light-sources situated on the ultimate lightcone of a hypothetical observer (which is its event horizon at Hubble sphere distance) have infinite redshift, except local ones which are gravitationally bound?
 A: 
Is it correct to say that all light-sources situated on the ultimate lightcone of a hypothetical observer (which is its event horizon at Hubble sphere distance) have infinite redshift, except local ones which are gravitationally bound?

Yes, that is correct. This horizon is called "Cosmic Event Horizon"(CEH). CEH represents the most distant object which we can receive information as $t \rightarrow \infty$. 
As $t \rightarrow \infty$ Hubble Sphere approaches to CEH. This implies that at $t \rightarrow \infty$ the redshift of the galaxies which are not gravitationally bound to us will approach $\infty$ ($z \rightarrow \infty$).
You can calculate the CEH by using 
$$\chi_{ceh} = c\int_{a(t_0)}^{a(t_{end})} dt/a(t)$$
or 
$$\chi_{ceh} = \frac{c}{H_0}\int_{1}^{\infty} \frac{da}{a[\Omega_ma^{-1} + \Omega_{\Lambda}a^2]^{1/2}}$$
since $\dot{a} = H_0[\Omega_ma^{-1} + \Omega_{\Lambda}a^2]^{1/2}$ for flat universe.
If you take $(\Omega_m, \Omega_{\Lambda}) = (0.3, 0.7)$, you'll find that $\chi_{ceh}  = 1.14\frac{c}{H_0}$
So the objects at a comoving distance about $16 Gyr$ are the ones which we can communicate now. We will never be able to communicate the galaxies which are further than this distance.

https://arxiv.org/abs/astro-ph/0310808
