Lara Croft can't be an objectification because Lara Croft is an object. She's trying, in typical woman fashion, to humanize an object, like a doll or stuffed animal. Saying sexy characters objectify women is the same as saying dildos objectify men.

The fact that real women have agency is what allows them to objectify themselves; by focusing their entire being down to one aspect (in this case, sex appeal), they remove their agency and become, to people consooming that aspect, an object.

I would argue that this is exemplified across celebrity culture. Famous people, maybe exclusively, become famous for a specific aspect of themselves, which objectifies them in the eyes of people. Fans then rehumanize them, but through projection of their own desires, rather than reality. This is why fans get so personally upset when their favourite celebrity does or says something they don't expect; the object is not behaving as imagined and it breaks the illusion.

I would argue that it's easy for us to separate objects and people until people start acting like objects while expecting to be treated as people.