here's a wild theory for you...

Maybe the sub is not a long range sub, so it is only used for trips to different points on the main island, and to the Hydra island. One of the places the sub can dock is the Looking Glass (this much we definitely know, because the diagram of the Looking Glass station has a picture of the sub docking in the moonpool opening)

So then how do people get to the island, when they think they are coming on the sub? How about this: there is a doorway, like a teleport doorway, somewhere on the Looking Glass station, that allows instantaneous travel between the station and somewhere near Portland, Oregon. The tell you that you need to be knocked out for the trip, like when Richard told Juliet, but that is just to cover up the fact that they have a teleportation doorway. (or maybe you have to be knocked out for the teleport trip - maybe you'd hurl your guts out if you were awake for it) Whatever the reason, you are unconscious, they take you "Through the Looking Glass" to the Looking Glass station (so that's where the name comes from) and then put you on the sub and take you to the dock where you wake up, thinking you traveled on the sub the whole time.

How about that?