Firstly, you should rip off all the laths as well; their thickness will be uneven (traditionally they used to be manufactured by an apprentice wielding an axe!) so anything you attach over the top runs the risk of being uneven too.
If the walls are going to be within a shower, then I'd use aquapanel behind the tiles - won't be trashed by water if any does get through - but anywhere else, plasterboard.
Thats pretty drastic, although the A1 class solution.
If you tile properly and seal plasterboard is in fact fine. If you have enough water ingress to turn plasterboard soggy, you have a serious wood rot problem as well.
Plasterboard applied via dot and dab is also well able to cope with an uneven surface.
I have to say that overall my favorite surface for building tiled bathrooms out of is MDF.
It takes screws, it stays pretty damned flat, and it can add a lot of stiffness that help stops tiles flaking off in flimsier studwork.
Re-plaster would be the proper way. Failing that either strip the lath and plasterboard, or if you don't want to do that you will need to dryline it using dot n dab. Take care to put the dabs mostly over the studs and noggings to eliminate as much flex from the mounting points as possible.
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