While the regular water-based eelies seem to move around just fine within their little ponds I've noticed that the Lava Eelies never seem to move. I'm not sure if this is an error with the lava eelies, the lava itself or something else but it is definitely happening.
This is an old bug, water-going monsters cannot swim in goo, ice, or lava. So they just sit still. Theoretically this means that if you spawned lava eelies in water they would move but I haven't seen this.