D&D 5E - Two-Weapon Fighting with a natural weapon?

My gut says this isn't allowed per RAW but just curious if there has been any ruling that would allow this:

If a race has a natural weapon (like Lizardfolk from Volo's), if you take the Attack action, can you then use a bonus action to attack with your bite? (assuming your main weapon is light)

The reason I ask is that the Lizardfolk's Hungry Jaws ability states it requires a bonus action (but does not require the Attack action).

Again, I believe the answer is technically no but it's something I would probably allow. Natural attack abilities tend to be a throw-away in most cases unless the character is without a weapon for some reason. This would at least make them a bit more useful.

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