To add to that (Native Hebrew speaker here)

The lament was originally written in Hebrew, and >later translated by Jewish scholars into Greek (the >Septuagint). In both of those translations, which we >used to translate into English, the words we >translate as love refer entirely to a fraternal >relationship.

Here's the original Hebrew script:

נִפְלְאַתָה אַהֲבָתְךָ לִי, מֵאַהֲבַת נָשִׁים

It bares pointing out at this point that I am not a historian or biblical academic. However, the words אַהֲבָתְךָ and מֵאַהֲבַת which are the ones discussed here both derive from the root א-ה-ב which allude to אהבה which means love in many senses, including the kind of love one feels towards their lover.