In his book, Hans Ørberg uses macrons to show longer vowel sounds, but it's not clear to me if this is reconstructed, ecclesiastical, something else, or if there are even differences between those vowels in each style of pronunciation. An example from chapter two is the name Iulia: Iūlia / Iūliī.
Strictly speaking, LLPSI doesn't require any particular pronunciation style: you're free to read the text in Reconstructed Classical, Ecclesiastical, Traditional English, or whichever you prefer!
However, the vowel length markings are generally associated with Reconstructed Classical pronunciation. In Classical times, the long vowels (ā ē ī ō ū ȳ) were literally pronounced for longer than the short ones (a e i o u y); there was probably also a difference in sound (though whether this was acceptable in high-class oratory or considered a Vulgar trait it unknown). In the Romance languages, the length difference eventually disappeared entirely, and the set of twelve monophthongs was reduced to seven.
So when mediaeval writers went back and tried to imitate the Classical style, they didn't really bother with the vowel lengths (since they weren't a familiar part of everyday speech). For the most part, a and ā were pronounced exactly the same, and the difference was only marked in writing when absolutely necessary (like to separate Rōma from Rōmā; the latter was often written "Româ", with a circumflex).
Later, linguists and classicists looked back at the evidence, and came to the conclusion that vowel length was important and deserved to be studied. To the Romans, it was an important distinction, and it separated various near-homophones (like alium "another", ālium "garlic", or anus "ring", ānus "old woman"). So vowel length has had a resurgence of popularity.
But the Ecclesiastical pronunciation, and most of the regional pronunciations like Traditional English, were codified long before that. They're less concerned with how the ancient Romans spoke and more concerned with how people have been speaking in more recent years. So (except for a few exceptions involving e and o) those pronunciations don't care about vowel lengths. If you're using one of those, you can safely ignore the long marks when reading.
P.S. For an extremely brief and simplified summary of vowels in Reconstructed Classical pronunciation, ī i ē e ā a o ō u ū y ȳ were something like
/iː ɪ eː ɛ aː a ɔ oː ʊ uː ʏ yː/. If you're interested in digging into this further, feel free to ask another question!