The kingdom of organisms that lack a well-organized nucleus and membrane-bound organelles is the Monera kingdom.

This kingdom is now considered outdated, and the organisms within it are now classified into two domains:

* Bacteria: These are single-celled prokaryotes, meaning they lack a nucleus and other membrane-bound organelles.

* Archaea: These are also single-celled prokaryotes, but they have distinct differences from bacteria in their biochemistry and genetics.

So, while the term "Monera" is no longer used, the organisms it encompassed still fall under the category of prokaryotes, which are defined by their lack of a true nucleus and membrane-bound organelles.