[wrholt]

The first word in your sentence should not have an accent mark (a.k.a. a tilde): él means "he", while el means "the".

Your sentence, "el hombre está listo para trabajar, pero su mujer no lo está" is equivalent to saying "el hombre está listo para trabajar, pero su mujer no está lista para trabajar".

Valid translations of your sentence into English are "the man is ready to work, but his wife isn't" and "the man is ready to work, but his wife isn't ready (to work)".

Spanish allows either repeating the object/complement phrase "listo/lista para trabajar" OR replacing the phrase with the neuter object pronoun "lo". Spanish prohibits omitting the object/complement except for the meaning "to be here/at a place/to be present".

In contrast, English allows either repeating (some) of the object/complement phrase, or omitting it entirely, but prohibits replacing the phrase with a pronoun.

A few other common Spanish verbs also require an explicit object in contexts where English typically omits them, including both "ser" and "saber". For example:

Are they from the US? Yes, they are.
¿Son ellos de Estados Unidos? Si, lo son.

Do/did you know that Mary and John got married last month? Yes, I know (OR Yes, I do).
¿Sabes/sabías que María y Juan se casaron el mes pasado? Si, lo sé/sabía.