Thanks for exploring ways to convert from CityGML to CityJSON using FME. As CityJSON is still relatively new, there are not as many resources available as for CityGML. I would recommend referring to the CityJSON Reader/Writer docs. There is also a recent CityGML webinar we gave in January that contains some CityJSON examples - see the examples download and the video at minute 35:00+. I would strongly recommend reviewing these resources before going much further.

In regards to your example, I would start with the acknowledgement that any CityGML/CityJSON workflow is by its nature challenging given the complexities of the data models involved, so there is usually a certain amount of trial and error in developing these. In your case, the first thing I noticed is that there does not appear to be any mapping from citygml properties to cityjson ones. Both writers require certain properties to be set on the geometries such as ids, lod names, parents etc. By convenience, some of these can be set as format attributes which in turn will be copied over the geometry properties by the writer. See the reader / writer docs under Writer Feature Representation for more info. Below is an example of some of these mappings as seen in the Citygml2Cityjson example from the recent Citygml webinar.

AttributeCreator mapping CityGML to CityJSON properties for building components.

That said, there does appear to be some limitations for the CityJSON v1.0 spec in relation to CityGML 2.0. The short summary is that CityJSON is meant to be based on the CityGML spec but in practicality should be considered a subset, not a complete implementation. The best I can determine from the available docs is that CityJSON v1.0 does not implement LOD4. The highest level of detail implemented is 3.3.

A quote from the academic paper published by Hugo Ledoux et al states that:

"The LoD4 of CityGML, which was mostly designed to represent the interior of buildings (including details and furniture), is not implemented. The main reason is that this concept will be revamped completely in the next CityGML version i19], and currently there are virtually no datasets having LoD4 buildings"

This may change in subsequent releases of the CityJSON spec given that CityJSON v1.1.1 corresponds with CityGML3, though I could not find any mention of LOD4 in the most recent version of the spec yet.

For more on this see:

TU Delfts refined LODs

CityJSON: a compact and easy-to-use encoding of the CityGML data model

CityJSON Specs