Why do lubricant eye drops need to be put into the conjuctival sac and is there any other way they can be administered?

Yes: It really doesn't matter where you put them, as long as they get in your eye. Most people find putting them in the conjunctival sac easier because you don't "see it coming" and the conjunctiva is less sensitive than the cornea. But you can drop them directly on your eyeball as well. Just be careful not to poke yourself in the eye with the dropper bottle.