lector - que lee
lector - lo que lee
Because it's an adjective. It's not a person or thing; it's the quality of being reading at the moment or having the habit of reading, which you can apply to things o people, as in, I don't know, "el topo lector" (= "el topo que lee").
This is how adjectives are defined. You can't say that rojo, for example, means "lo de color encarnado", because you would be defining an adjective in terms of a noun. So you say "rojo" means "de color encarnado". The (sub?) phrases "de color encarnado" and "que lee" have adjectival functions.
Now, it's true that "lector" is often used as a noun. If you regard it as such, "el que lee" is an adequate definition.