This really is no true equivalent to a JDBC driver if by that you mean something that works in a similar way. The sql style interface provided by NotesSQL and the JDBC driver was always severely limited.
To directly interact with the data with java you need to use the Notes java api using Notes.jar (local) or NCSO.jar (remote IIOP). This gives you a notes style access to the data. Your data is organized as databases of documents containing items. The documents are indexed into views and an individual document can be indexed by multiple views. There are also various built in search facilities.
If you just need to provide external access to a relatively fixed query a web service built into the application is a good way to go. Internally this would use the native notes api (java or lotusscript) and you'd probably want to get the developer of the database o do that for you.
If you really need to have free access to the data and want to query it with SQL you will have to export it to an RDBMS through a number of tools and some of these can keep your data in sync. Since there is no generic way to look at Notes data as simple tables you need to configure this export to match the application requirements.