Great, good to hear it!
The 'client library' they're referring to here is just the connection software. For example, the ODBC drivers you have already installed.
They are referring to a very specific situation there, and chances are you don't have to worry about it.
Normally, LEI is installed "onto" your Domino installation, and LEI becomes an add-in task to Domino. However, there is an option, if you wanted, to make LEI its own standalone application. It still requires Domino but operates independently from it. If you chose to do this, and if you put LEI and Domino on different machines, you would have to install the connectivity software (such as ODBC) on both the Domino machine and the LEI machine.
You only need to worry about that part if you are specifically doing this. Otherwise, LEI and Domino will be together in one place, and you only need to install the connectivity software once.