Historically (for interior paint) you would use regular limewash in dry spaces and add casein/milk in high traffic/wet spaces. It works in a bathroom but wouldn’t hold up in a shower (for that you would want to use “tadelakt“ - especially if you’re going for that Aman spa look).

The contemporary solution with modern limewashing is to use “mineral shield” - it uses silicone instead of casein - it makes water droplets bead up but still lets water vapor breath through.

It also doesn’t flatten out the nice velvet texture one gets with limewash paint from the calcite crystals.

That said, it’s extremely obvious if one touches up a patch of wall with limewash. No two batches are the same color unless you’re going pure white and even then…