Lotus Notes database encryption uses a user’s public key to encrypt the database. And the user’s private key is used to decrypt the database. Depending on the version of Notes and if you have a PKI configured, then you will just need to configure your Notes client to get your certificates from the PKI. If you do not have a PKI you might have the private key stored in the Windows Certificate Storage, which you will then need to export as a PKCS#12 file and then you can import it into your new installed Notes client.
*** Added *** Your Notes ID file contains the certificates and this should be copied from the Data (C:\Lotus\Notes\Data or similar) drive. When you open Notes it should ask you for a password, cancel until it asks for a file, then select the file you copied and enter your password.