Krudder64 since you have the original pass phrase used to create lobstr vault than you should be able to derive the private key in any standard BIP39 tool to multi-sign the account in stellar laboratory.
Update, it just occurred to me you've said the passphrase isn't returning the public key from the first install of lobstr vault in which case you may have written down the pass phrase incorrectly. However if that's not the case an outside guess is that on the 2nd install vault is seeing the key from the first install then moving down to another address on the keychain. The only way to tell would be to enter your passphrase in a BIP tool and see if the original key is the first one in the chain.
My apology, I was speaking to your other post that resonated with my original experience using lobstr vault in which the protected account didn't appear in vault until the following morning after installing.