I just found out about Lingua Latina: Part I, Familia Romana but it seems too good to be true, can you
really learn Latin with it, just by reading?
I don’t know if you’ll be able to pick up, say, Martial, and read it effortlessly, but I can say that I’m up to chapter 27 and it gets easier and easier to understand the Latin. Try it, since the first few chapters are online.
Lingua Latina Pars 1 is a very good book. However, many here on this forum suggest using Lingua Latina as well as a more traditional textbook.
I’m interested in reading history in Latin. Do you think Lingua Latina would adequately prepare me for Livy or even Medieval latin?
Since Lingua Latina Pars II is a lot of adapted Livy, I would say that your expectations are not far off mark.
The last chapter of LLPSI Volume 1 does teach you how to read Martial. 
I’m working through this book right now and am really thrilled with it. I wouldn’t say you learn “effortlessly” as it requires strict attention and effort to understand the subtleties of Latin no matter how you learn it, but what it does is contextualize the learning process via a storyline. You begin reading the story immediately, with no preparatory material whatsoever. Each chapter introduces at least one new grammar point and a good chunk of vocab. At the end of each short chapter, there is a review, in Latin, of the grammar that was introduced, followed by three “Pensum” exercises. I would recommend working through the exercises to solidify what you learned before moving on to the next chapter. Pensum A has you fill in word endings in a short summary paragraph, Pensum B is fill-in-the-blank for whole words in a second summary paragraph, and Pensum C is a series about 10 to 12 questions concerning the chapter you just read. The repetition and adherence to the piece of the storyline you just read make the exercises easy to do yet worthwhile as grammar/vocab reinforcers.
I will say that having knowledge of Latin or a modern romance language makes this book tons easier than it would be for an English speaker with no knowledge of Latin or a related language, however, the latter is who it was written for, so almost all of the words used in the early chapters are recognizable in English as loan words or close parallels of loan words from Latin and it’s offspring to English. Take the first lines of Ch. II: “Iulius vir romanus est. Aemilia femina romana est.” Well, if you relate “vir” to “virile”, you’ll know that “vir” means man. If you relate “femina” to “feminine” you’ll know that “femina” means woman. There are lots of line drawings interspersed in the chapter texts as well as on the margins to help you understand what’s going on. The margins are also chock full of explanations of new vocab with smaller line drawings and grammatical clarifications with diagrams and small case/verb tables.
You can also buy a workbook for more exercises and several study guides that go with the main book. It’s a far cry from copying endless conjugations and answering questions with no particular context, as you may find in some Latin textbooks. I’m exited about the possibility of going beyond early-beginner Latin proficiency that seems possible with this method. I’m only a few chapters in at the moment, but I can imagine that by the end of book one I’ll be able to write e-mails like this all in Latin My plan is to go all the way through book two as as well. Fellow Textkit members are welcome to contact me if they want to compare notes or form online study groups.
Valete.
I am an adult learner studying on my own. I’ve looked at a lot of resources, but I’ve found that I use Lingua Latina more than anything else. The narrative pulls me in and the need to puzzle out the meaning engages me. I will sometimes read well beyond my understanding to see what I can make out, or I will dig through the marginalia and see something completely new.
I keep a dictionary handy and I work with a grammar when I have time and interest, but they are supporting tools. It is the challenge of working out the story that keeps me coming back.
Given that the biggest challenge I face is the number of competing interests, that draw is absolutely critical to making any progress.
Cheers,
Ivanus