As far as I can tell, either would be fine.
The Google Ngram Viewer shows the following frequencies for "the underworld" and "the Underworld":

Lowercase is more common overall. Now, that's not taking context into account. I would imagine that "the underworld" would be very strongly preferred in contexts like "the underworld of crime" or "the underworld of the city", but it may be less strongly preferred in other contexts.
Another Ngram Viewer chart that seems relevant:

This should exclude examples where "the underworld of..." is used. It still looks like lowercase ("the underworld") is more common in this context, so I'd say that is an acceptable choice. But I would say that the uppercase variant "the Underworld", although apparently less common, seems frequent enough to also be an acceptable choice.
Related: Shouldn’t “Heaven” and “Hell” be capitalized, as they are the names of places? and Should “Hell” be capitalized?; also more distantly What is the correct capitalization of the words earth and moon? and Capitalization of the word universe