Plus, why would Lash want Dresden suicidal?
She wouldn't. She'd want him to survive. Which he wouldn't do if he couldn't save Maggie. And he'd have a hard time doing that with his spine broken (for one thing, Chichen Itza probably isn't ADA accessible; way too many stairs).
The seven words weren't, "This is your fault, so kill yourself." If Lash is doing the whispering, the intention was probably more along the lines of guilt tripping him into getting more power--preferably through her, but if not, keeping himself alive means she survives either way.
She probably either didn't see the suicide coming, knew that it wouldn't work, or didn't have enough power to talk him out of it without making it obvious she was still around.