On the other hand, unlike you I do not believe that any of the transformational prestige classes require the character to gain the LA of the template granted by the prestige class.
To be perfectly clear on my position:
IMO the RAW on most transformative PrCs that grant a template is somewhat unclear (and ridiculous FAQ responses like the Dread Necro one saying the phylactery doesn't do anything don't help). It's a valid reading in most cases that the LA doesn't apply, and it's the reading I'd personally use because it's the most sensible.
Walker in the Waste is different in its transformative element in two ways:
1) the transformation isn't automatic upon getting the level, but requires a ritual that can't be done alone,
2) the transformation uses a template (rather than simply being handled by class features), but the template can only
be applied to people who've completed the PrC.
Furthermore, unlike most transformative PrCs, there's an explicit example of someone who's completed the PrC, and they are listed with an LA. I don't really see a way to claim that WitW 10 -> Dry Lich doesn't give you the LA when we can plainly see a sample WitW 10 -> Dry Lich in the book and he has the LA.
The above is my interpretation of RAW, not my personal opinion on what makes sense or is reasonable. If I were DMing and a PC went Dry Lich, I'd houserule away the LA - it's just plain silly.