That's for sure a vocal thing. Her voice sounds like that with those consonants.

Compression will only make it more obvious. That Lana record was tracked with a Wunder CM7 into a BAE and then a CL1B so the gear is really not the issue. I don't really think it's an issue at all but if you don't like it then you should try recording with a dynamic or a ribbon, because those sounds will be brought forward by most condensers.

Yo could also try something darker like 414 B-ULS or a Manley Silver.