Before I get into what changes can be done to the hellstar, let's discuss what makes the two items in question different. Being in the dark school, hellstar is an in school option for warlocks and necromancers in both arena and academy. 1 spellbook point for an item that burns 5/12, could be a good mix up tool to throw your opponent off when your book doesnt focus on burns. Dragon's lance is in the fire school, giving in school bonus to again warlocks but also elementalist and monk due to martial subtype. With a 50% burn roll, an ability to guarantee a burn, and held item options, Dragon's lance does look like an all around better option for a fire mage to use, but for a nature mage who wants to switch things up hellstar wouldnt penalize them in the SBP department.
So there are a couple things about hellstar that could be changed to set it apart from dragon's lance.
1. Grant hellstar the unavoidable trait. There would need to be a mana readjustment for this equipment, but it would be more in tune with the morning star. It cost more mana because it also burns unlike morning star which is just unavoidable.
2. Better burn chance on hellstar than dragon's lance. Pretty straightforward, reduce hellstar base burn roll equal to or lower than dragon's lance burn roll. IMO it would need to be lower than to give it some appeal. Firestream is 4mana 4dice 6+burn, if we brought hellstar to 6+ from 8+ then we would have a choice between cast an attack spell or cast hellstar and attack for almost similar value.
3. Hellstar needs flame damage added to its attack bar. Having a higher burn roll than dragon's lance but having the benefit of being flame damage would balance out these two items especially for the Arena crossover. Making hellstar a cheap not as effective lash of hellfire would be a good way to revitalize this item. It would gain benefits of fireshaper ring and attacking flame+ targets, but it would be confusing as to how a nature mage has a weapon on fire but doesnt have a penalty for having it.
These 3 options are all worth pondering over for a possible errata to hellstar. As the game progresses and more cards are added some might get completely overshadowed. I feel hellstar was forgotten when they made dragon's lance, and it was left in a bad state compared to its newer model.