Different ancient translators had different translation philosophies. Some were very rigid and always used Greek word X for Hebrew word Y. Others were more dynamic. We can actually use these philosophies to determine when different translators are responsible for different books. For example, the Greek of Numbers is very literal (except the name of the book. The Hebrew is Bmidbar -In the Wilderness -, but the Greek is Arithmoi, which is where we get the name Numbers). The LXX of Numbers is Greek vocabulary with Hebrew syntax. This also works very nicely for text criticism. When that pattern holds, we can be more certain that the Hebrew source was the same as in the BHS today. When the pattern breaks, either there was a different Hebrew vorlage or the LXX Numbers was miscopied at some point.
IIRC, Exodus is not that way. Exodus has less one-to-one and more what-word-best-translates-this-Hebrew-word-in-this-context attitude. Genesis in the LXX shows both attitudes. Gen 1-11 are very much in the word-for-word attitude, even so far as the waw conjunction always being translated with kai. Gen 12-50, however, uses both de and kai for the waw conjunction. Some books even achieve paraphrase status.
The question comes down to what is the translation philosophy of the Greek translators of Song of Songs? Was the translator one of those who always uses the same Greek word for this Hebrew word? Or was he more contextual? Or even was he reading it allegorically?
As I do a word search on 'ahab I see it is used 11 times in Song of Songs. In the Septuagint of Songs, 'agape also appears 11 times. There is a one-to-one correspondence. agape is the only word used in Song of Songs to translate 'ahab.
Though I can't be sure of the whole philosophy without a more extensive analysis of the LXX of Songs, it appears that with 'ahab at least, the translator had a one-to-one correspondence in mind.