In the Wikipedia article about lightining, the following explanation is given about the electrification process in clouds:
The details of the charging process are still being studied by scientists, but there is general agreement on some of the basic concepts of thunderstorm electrification. The main charging area in a thunderstorm occurs in the central part of the storm where air is moving upward rapidly (updraft) and temperatures range from −15 to −25 °C (5 to −13 °F); see Figure 1. In that area, the combination of temperature and rapid upward air movement produces a mixture of super-cooled cloud droplets (small water droplets below freezing), small ice crystals, and graupel (soft hail). The updraft carries the super-cooled cloud droplets and very small ice crystals upward. At the same time, the graupel, which is considerably larger and denser, tends to fall or be suspended in the rising air.
The differences in the movement of the precipitation cause collisions to occur. When the rising ice crystals collide with graupel, the ice crystals become positively charged and the graupel becomes negatively charged; see Figure 2. The updraft carries the positively charged ice crystals upward toward the top of the storm cloud. The larger and denser graupel is either suspended in the middle of the thunderstorm cloud or falls toward the lower part of the storm.
This mechanism seems to rule out the possibility of lightning in absence of a condensed phase (liquid droplets/solid crystals). That makes me wonder, is lightning truly impossible in stars hot enough to be fully gaseous, like our Sun? Or could a alternative mechanism generate lightning in such environment.
Even in absence of any alternative mechanisms, I think lightning still could form at least in small, cold stars, or in old brown dwarfs. What would be the size/age threshold?