"She had already assumed it."
Translation:Ella ya lo había supuesto.
"asumir", on its own, has the same meaning as "assume" when they both mean "to take on" (or similar meanings), e.g. "to assume responsibility". It is only when you add the preposition "que" (asumir que) that it has the same meaning as to assume/make an assumption. Hope that helps. But, even in the first case, it should be accepted: "I was going to tell her she had to take on the responsibility, but I was too late: she had already assumed it." So if you have time to report it with an example, you should.
I think this should be correct as well and reported it: "Ella ya lo había asumido"