if a laboratory balance accurately measures mass on the earth, can it accurately measure it on the moon?

Yes, a laboratory balance can accurately measure mass on moon also.

Explanation

The work of laboratory balance is to determine the mass of an object.

Generally, a laboratory balance consists of two pans and it determines the mass of an unknown object by reference with a known mass object.

Also the mass of any object tends to remain constant in all conditions.

The mass has no effect due to gravitational force unlike weight. So the laboratory balance can work accurately in any environment as the mass will be constant in any case.

Thus, if a laboratory balance measures mass accurately on earth, then it will measure mass accurately on moon also as mass is not dependent on gravitational force.