KYLE: Is it possible for an LXX based text to have a bible (no modifier) index?

Possible? Yes. Desired? No, with a caveat.

There are a few factors at play here. 

1. Age of the resource. We've gotten much tighter on what is and isn't supported. It used to be that we could ship a resource with milestones that are unsupported in a verse map (i.e. index). These days we need to be much more precise when shipping a resource with a Bible index.
2. Information provided in the resource. When choosing a verse map we look to clues within the resource. Best case scenario is that the title, copyright page, or front matter identifies the verse map explicitly. From there we fall back to a few default verse maps depending on the language. Bible is the default for English. From there we run some validation to make sure nothing is unsupported. Our validation is robust enough that if something fails it provides suggestions but its not uncommon to require further investigation.

I only looked at one of the books in the Temple Series. I didn't run any validation on it but based upon a cursory look at the front matter, it's likely it would end up with a Bible index even today.