The only reason Lanfear would be killed by the Shadow would be if she tried something, much like when Moghedien tried to use the Power in the Pit of Doom, or if she tried to kill Moridin. She's impulsive but she's never gone after another Chosen before. In both cases her death would be the final one.

Killing Lanfear provides little benefit to the Shadow. It takes a long time for a Chosen to be resurrected and requires a search for a body and other effort on the Dark One's part. We've also seen that people like Osan'gar and Aran'gar struggle with their new bodies and identities. None of this is beneficial and only works because it serves the Shadow better than the Chosen's actual death.

I find it almost impossible that she was killed to remove her beauty, or to provide some sort of fall from glory. Merely disfiguring her like Sammael would be sufficient. Besides that, the Shadow doesnt work like that... Forsaken failures are rewarded by the attentions of SH. We've seen it wilth three of the female Forsaken now. There's no reason to suspect that Lanfear would be any different.