If they don't bring Michael C Hall over with the show, they're going to have their work cut out casting the lead. Difficult to imagine any of the usual suspects like Killian Donnelly. Michael Xavier or Richard Fleeshman in something like this. They need to cast someone really edgy - Paul Kaye perhaps or Matt Smith (following some intense vocal tuition).
I'm not familiar with the Royal Court, but could it be a possible venue? Since the teaser came before the live stream of one of their productions?
That was the thought I had too. It's a very flexible space, suited to all kinds of productions (they've historically done very few musicals, FWIW).
Rocky Horror played at the Royal Court IIRC. Considering The Almeida, the Dorfman and Hampstead have all successfully had musicals in the last few years and all three have similar capacity to the Downstairs theatre, I think it would be a good theatre for Larazus.
Considering Lazarus has its own website, that suggests to me it's going straight to the West End (Arts at the smallest). Places like the Royal Court, Almeida, National, Hampstead, etc have their own very comprehensive websites so it would be very unusual to start with an external website if it were going to such a venue. (And considering how the women were written in Lazarus, I somehow can't see someone like Vicky Featherstone welcoming it with open arms...)