I understand that the normal "single quote" marking indicates stress, but what about the lowered one?
The low stress mark
ˌ is simply used before a syllable to indicate a lesser degree of stress than the high stress mark
Different theories or descriptions of English phonology recognize different "levels" of stress and different names for them. In Balogné Bérces Katalin's "The Pronunciation of English", syllables like the "gran" in "pomegranate" are described as having "tertiary stress".
According to Balogné Bérces, a syllable with secondary stress always occurs earlier in a word than the syllable with primary stress (for example, the first syllable in the word "derivation" has secondary stress, and the third syllable has the primary stress). There are a few other conditions that Balogné Bérces identifies as necessary for secondary stress that I won't get into here, but that you can see if you look at the linked document. Syllables in other positions with unreduced vowels are described as having "tertiary stress".
Although they can be distinguished in theory, many dictionaries transcribe "secondary stress" and "tertiary stress" the same way (or they use
ˌ before some syllables with "tertiary stress", and no stress sign before others). Actually, the use of any stress marker at all is probably redundant for this word, because the use of the symbol "a" for the vowel indicates that it is not reduced. As far as I know, there is no accent of English where |ˈpäm(ə)ˌgranət| really contrasts with |ˈpäm(ə)granət|.
There is a relevant post on John Wells's phonetic blog, "irritating hamburgers", where he argues that it is unnecessary to use any kind of stress marker in the transcription of the second-to-last syllable of the word "irritating", although he notes that such transcriptions are in fact used by some sources:
native speakers tend to perceive the penultimate syllable [of irritating], teɪt, as being more strongly ‘stressed’ than the final syllable ɪŋ. But what they want to call ‘stress’ is arguably no more than a way of saying that the vowel is one of the strong ones. Actual rhythmic beats following the main word stress accent are all pretty optional, which is why the British tradition is not to show any secondary stress in words like this: ˈɪrɪteɪtɪŋ, not *ˈɪrɪˌteɪtɪŋ. The alternative tradition, usually followed in the States and (for example) Japan, is to recognize a secondary stress on the penultimate, írritàting.