Long‐lived, persistently active lava lakes are rare but have been studied extensively, because they may provide a natural laboratory for studying magmatic convection in basaltic and other low‐viscosity volcanoes. However, lava lakes differ from other volcanic systems in various ways, particularly geometry: the presence of the lava lake requires a sudden and significant flaring of the conduit. The goal of this paper is to advance our understanding of the effect that a sudden increase in the conduit width has on the stability of large gas slugs and bubbles ascending from the plumbing system. We investigate this question by linking analogue laboratory experiments to direct numerical simulations in two dimensions. We find that the rapid change in the geometry associated with the transition from the conduit to the lava lake causes large gas slugs to break up. The non‐dimensional regime over which we observe the breakup depends sensitively on the flare angle of the lava lake and the importance of inertial effects in the flow, implying that the geometry may sensitively affect degassing‐related eruptive activity at open system volcanoes. Applying this idea to the likely geometries and viscosities of actual lava lakes, our study suggests that all lava lakes except Erebus fall well within the regime where large gas slugs are prone to breakup.