Translation:I only remember that the lips were cold.
I can't tell, but I feel this sentence goes better without "my". Perhaps because there is nothing implying that the most obvious owner is myself.
Different from "feeling", "feeling pain" (which obviously puts me as the owner). Or doing actions, getting hurt. Things that clearly go better with me as the owner.
This sentence somehow separates the lips with "they were cold", different from "I had cold lips".
In Latin, labrum is neuter. Several other such nouns wind up in Italian split between masculine and feminine, e.g. l'uovo/le uova. For orecchio, there are two plural forms: gli orecchi and le orecchi. For braccio 'arm', one speaks of folded arms (a braccia conserte), but in a metaphorical sense, e.g. the arms of a lake or river, it's i bracci.
I think markeckstein is referring to the verb ricordarsi (http://italian.about.com/library/verb/blverb_ricordarsi.htm)
Ricordarsi is a reflexive verb. Why is the verb being used in a non-reflexive manner?
I don't understand why you think that this should be reflexive? Ricordare means to remember ; I only remember (ricordo solo ) that (che) the lips (le labbra; remember the end of labbra doesn't change, just the infinitive to make it plural) were (erano) cold (fredde cold, plural) because the lips are plural and it's an adjective. I hope I have explained it well enough for you without being a smart aleck!