The Encyclopedia Talmudis has a complete article on bee honey (under dvash) and why it is kosher. As part of the article it shows the difference between bee honey and milk of a nonkosher animal. The honey is carried by "baskets" outside the bee and is processed by "external" processing. That is, it is chewed by the bee, mixed with saliva and regurgitated. It is never digested. Milk on the other hand is considered as if it is derived from the "blood" of the animal. That is by "internal" processing. It is created internally from digested nutrients.
In this particular case, just because the bees set up there hive inside the lion's body does not make the honey considered as if it was part of the lion. The bees and the honey are totally separate objects. If it had been a deer, which had tumas neveilah, then he would not have been able to get to the honey while the deer was tamei. Once the tumah dissipated (after the deer was no longer edible), he could have gotten it. Since a lion is not a kosher animal, it was not tamei and he was able to take the honey. (Besides it was quite a while later).
Note that bee honey is not kosher because of a takkana but was known to be kosher from the beginning. For example the case of Yonasan ben Shaul Hamelech taking some honey during the war with Amalek. The only objection was the oath his father had made. It was well known and accepted that bee honey was kosher. Similarly, we see here that bee honey was kosher. The Talmudic derivation is only to point out how we know this.