Why does Volcano Lightning occur?
To actively take measurements from the mount of an erupting volcano is not practical, so the mechanisms are often modeled in a laboratory, such as what was performed in the article Experimental generation of volcanic lightning (Cimarelli et al. 2014), who determined that volcanic lightning is controlled by the dynamics of the volcanic jet and how much fine particulate matter is present.

A key observation that the researchers found was that the movement of clusters of charged volcanic ash and other particles form to generate an electric potential, critical for the generation of lightning. An idealised diagram of this process is shown below:



Image source

As to why the particles themselves are charged was researched in the article Electrical charging of volcanic ash (Aplin et al. 2014), which suggests the ash becomes charged through fractoemission, triboelectrification, and the “dirty thunderstorm” mechanism, and the authors also suggest that natural radioactivity in the volcanic emissions may play a role.