I was curious if there was any way to fannagle getting two people into a locked room with this, so I asked the dev team. The short answer is no.
The long answer is the email below:
Thanks for the questions! For the answer to your question about moving into the Vault with Safeguard: The text on the Vault states that you cannot enter the Vault unless you control the [Elder Thing] Key. The text on Safeguard lv 2 allows you to move to a connecting location with an investigator AS they move. Here's the breakdown:
Since your investigator moves with your friend to the Vault simultaneously, and the Vault specifies you cannot enter unless you control a specific key, you are unable to move with your friend as they move to the vault, since you don't control the key, and the "cannot" in the Vault's unrevealed side is absolute. The wording on Safeguard also doesn't trigger off of your friend declaring their intention to move into a location: it only triggers as they move into the location. As a result, you can't use Safeguard lv2 to enter the Vault alongside your friend under any circumstance (in the situation you posited), because you don't control the [Elder Thing] key. Additionally, if you have the [Elder Thing] key, you cannot Safeguard with your friend who doesn't have the key into the Vault, as they cannot move into the Vault unless they control the key in the first place.
Please note, though: with the wording on Safeguard lv 0 ("After another investigator moves from your location to a connecting location, exhaust Safeguard: Move to that location."), you are able to follow your friend who controls the [Elder Thing] key into the Vault, as the timing of the move occurs After​ they move into that location. So oddly enough, Safeguard lv 0 is more helpful in this situation than the upgraded version!
Thanks for playing!