You can actually just create a new Search Filter.

This example inherits the existing Analytic Items View and adds a filter to show only those Analytic Lines where the Customer Invoice is paid:

<xpath expr="//filter[@name='month']" position="after">
    <filter name="move_id" string="Invoices that are Paid" 
            domain="[('move_line_id.move_id.payment_state', 'in', ['paid'])]"/>
</xpath>

The domain of the filter goes through the Journal Item linked to each Analytic Line, then through the Invoice to the Payment State.