It may be a while before productions can resume in America again, but there are already some countries in Europe, particularly the UK, that have been lifting production bans with some new rules set to be followed. The Batman was actually shooting in London before the lockdown, and there looks to be no plans to resume anytime soon.
According to Deadline, The Batman and Fantastic Beasts 3 are still going to remain on hiatus till further notice. If anything, they could just follow the leadoff The Matrix 4, which is planning to resume production sometime in July.
Though bans have been lifted, it's worth noting that it could still be hard to get production crews back in London for shooting. I'm pretty sure there will be a requirement for every crew member to be COVID-19 negative before they enter the country, and there has to be rigorous sanitation of the sets before any work can begin.
If anything, I think it's safe to wait it out a bit more for now. While I can imagine that a lot of people are itching to get back to work, going out of quarantine too soon could lead to a second wave of the coronavirus if they aren't too careful.
For now, I think the cast and crew of The Batman should just hang tight. I'm sure Robert Pattinson is currently enjoying not having to work out daily to keep in shape.
The Batman is set to hit theaters on Oct. 1, 2021.