I'm sorry to see that nobody responded to your question in a timely manner, but let me try to offer some assistance at this point.
First, it probably helps to reserve the terms 'long' and short' for vowels (or diphthongs) and note that they refer to the amount of time taken to pronounce these sounds. For the purposes of establishing how words fit into the metre it is now common practice to use the terms 'heavy' and 'light' to describe syllables. This helps to avoid an otherwise confusing ambiguity in the terms.
Now, to begin, I'll point out what it probably obvious: since ω and η represent long vowels, syllables containing them generally count as heavy for the purposes of the metre; ο and ε represent short vowels and so syllables containing them generally count as light for the purposes of metre; syllables containing a diphthong, which requires about the same amount to time to pronounce as a long vowel, generally count as heavy for the purposes of metre. This means that only the vowels α, ι, υ are capable of representing either a long or short vowel and so might need to be marked in a dictionary.
As a further hint, any vowel carrying a circumflex accent must be long.
Now, a quick reminder about the metre used in Homer, the dactylic hexameter. The basic dactylic foot comprises one heavy syllable followed by two light syllables, often indicated as -uu (when the more comprehensive symbols might not be available in one's font). Note that the term dactylic derives from the Greek δάκτυλος, finger, because a finger consists of one long joint followed by two short joints.
As you have probably learned from Pharr's description, a heavy syllable can substitute for the two light syllables in the foot giving -- (known as a spondee). The sixth foot in the verse is actually a heavy syllable followed by just one more syllable, either heavy or light. (It has often been explained that the slight pause at the verse end allows a light syllable to occupy the same amount of time as a heavy syllable, thus in effect always creating a -- foot at the end of every verse.)
Knowing just these basic facts means that you can often accurately 'guess' whether a vowel is long or short based solely on what the metre requires. In fact, this is how the length of many syllables containing α, ι, or υ were determined in the first place.
As it happens, Cunliffe's lexicon and the various incarnations of the Liddell and Scott dictionary do mark the long vowels. By convention, all unmarked instances of α, ι, or υ are short. The other vowels and diphthongs are inherently long or short as indicated above.
A word of caution: although the diphthongs αι and οι, when final, are counted as short for the purposes of determining the placement and type of accent in a word (except in optitive forms), they are counted as long for purposes of metre.
Finally, we come to the main reason for using the terms heavy and light for syllables rather than sticking with long and short. A short vowel, followed by two (or more) consonants, or a double consonant (ξ = κσ, ψ = πσ, ζ = σδ) counts as a heavy syllable. Older grammars referred to these cases as being 'long by position', or that the consonant cluster 'made position'. Many students came under the mistaken impression that the short vowel would now receive a lengthened pronunciation and magically become 'long' which is not the case at all. However, if you pronounce these combinations slowly, you will find that it does take longer to sound a vowel + two consonants than a vowel + one consonant, thus elongating it into becoming a heavy syllable.
Also make careful note that the consonants needed to 'make position' (change a syllable with a short vowel into a heavy syllable) can be in the same or the following word. Remember that in the earliest forms of Greek writing there were no spaces between words so these consonant clusters were determined strictly by their impact on the pronunciation, regardless of which word they were in , and also bearing in mind that Homer's works derive from an oral poetic tradition.
If you use one of the online versions of the Liddell and Scott (and Jones) dictionary, generally referred to as the LSJ, at the Perseus site, you will encounter notations using '_' to represent a macron (long mark) and '^' to represent a breve (short mark). For example, looking up λύω one sees "fut. λύσω [υ_]" meaning the upsilon is long here. Or, "pf. “λέλυ^κα” " meaning that the upsilon is short. Or, "aor. “ἔλυ_σα” " meaning the upsilon is long. The '_' is written inline here because the upsilon does not carry an accent while in the earlier case it did. This is a common limitation of fonts which support polytonic accents but not in combination with the macron or breve, which is not part of standard Greek orthography.
Naturally, there are additional complexities to the metre and the various rules used to accommodate words which would otherwise be disallowed in the hexameter. Pharr does give an overview of many of them so you should have enough information at this point to accurately determine the correct scansion of most Homeric verses; certainly, the first 100 verses of book Α of the Iliad which Pharr recommends for practice.
If you see this post and are still working on metrical issues, please post any further questions or problems you encounter. When I went through Pharr's book I did take the time to work out the scansion of the first 100 verses, by which time it becomes pretty automatic, and I did find that working it out added significantly to my enjoyment of the poetry. I hope you have a similar experience.