I have not progressed this far in Latin, but this is based on the research I've done to plan my own future Latin progress.
First, there are two readers designed to accompany LL1 and are keyed to the chapters in it:
Lingua Latina: Colloquia Personarum (keyed to first half of Familia Romana)
Lingua Latina: Fabulae Syrae (keyed to second half of Familia Romana)
In addition, there is a free downloadable supplement they put out called called Fabellae Latinae.
Second, the company that publishes LL also publishes readers and supplements
to complement the student's progress in LL1:FR and LL2:RA.
Easy (for those who have finished FR):
Caesaris: Commentarii De Bello Gallico
Plautus: Amphitryo Comoedia
Intermediate (for those who are working through RA):
Ovid: Ars Amatoria
Vergilii Maronis: Aeneis
Petronius: Cena Trimalchionis
Hard (for those who have finished RA):
Sallustus & Cicero, Catilina
Hope this helps!