Can lossless audio be wirelessly transferred via Bluetooth?
Yes and no.
Yes: it's a binary connection so technically it's feasible provided the bandwidth of the connection is high enough, but you would have to write your own low-level software.
No: None of the current Bluetooth audio protocols supports that since it can't be done reliably over a large number of setups and applications. A lossless audio stream requires typically about 1.1-1.2 Mb/s which is at the limit of what Bluetooth can. There are lots of various connection types (depending on distance, signal to noise ratio and version of the BT protocol) and many don't have enough bandwidth or it's right at the edge of their capabilities.
See for example: https://darko.audio/2020/01/ces-2020-bluetooth-sig-unveils-le-audio/
If no, what aspects would we improve to be able to wirelessly transfer lossless audio via Bluetooth?
You would have to join the Bluetooth Audio Working group and start lobbying for a change or added feature. The working group is fairly pragmatic: For the foreseeable future Bluetooth bandwidth will be a carefully managed commodity. The perceived benefit of lossless audio is very small as compared to the massive increase in bandwidth requirement. Hence it's only a fringe use case and the majority of the industry is unlikely to support it.