If someone was expecting to hear a word pronounced in the same way as light - in other words as /laɪt/, and they then heard this word, they may very well mishear it.
The word is actually /laɪð/. The sound you hear at the end there is a voiced fricative, just like the sound /v/, but it is a dental fricative. We make it with our tongues touching the back of our teeth. It is the same sound we hear at the beginning of the word then. This sound is most frequently heard at the beginning of 'function words', the types of word you would study in grammar lessons:
- this, that, these, those, them, their ...
Sometimes, however, we hear it in lexical words (the kinds of words we often look up in a dictionary). At the ends of lexical words a particularly common spelling for this sound is -the.
As at least one commenter has said, there is often an alternation between a noun of the same root ending in -th, pronounced with the unvoiced dental fricative, /θ/ ( - the sound at the beginning of the word think), and a verb ending in -the, pronounced with its voiced counterpart /ð/. Compare the nouns:
- wreath /ri:θ/, sheath /ʃi:θ/
and the verbs:
- wreathe /ri:ð/, sheathe /ʃi:ð/
However, as will be seen from the Original Poster's question, this ending occurs with other parts of speech too. The target word lithe, with which we are currently concerned, is an adjective. We can also find nouns such as swathe/sweɪð/.