Within the context of Serial Experiments Lain, metaphorize (メタファライズ) is to project a digital incarnation of one's personality into the Wired. Lain is highly admired in the Wired partly because of her ability to metaphorize herself so completely.
The word is used several times in the original Japanese dialogue of the anime as well as at least once in the English dub, and even flashes across the screen once in Layer 07, misspelled. In the English dub and subtitles, it is sometimes mistranslated as "metamorphosis," or some variation thereof. This might be because "metaphorize" is not a commonly used word in the English language, not even appearing in most dictionaries.
The word was used in the same sense in Alice in Cyberland, a game and OVA written by Chiaki Konaka.