She is a lady and should be treated as such.

Literal

She [topic-は] lady is [and-であり], that-way treated-should-be.

A formal declarative built on three elevated structures: であり (the formal continuative form of である) links two predications, the passive 待遇される focuses on the treatment she receives, and べきである frames it as moral obligation. 淑女 (しゅくじょ) is a literary word for a refined or graceful woman — more formal than 女性. そのように (in that way / as such) refers back to 淑女, connecting the two halves into 'she is a lady, and ought to be treated accordingly.' The whole register feels appropriate for an op-ed or formal social commentary.