The problem wasn't Jacen, it was Anakin
The original story outline of the New Jedi Order series was that Anakin was intended to become the new hero of the Jedi Order, while Jacen was meant to die along the way. Lucas's objection to this wasn't that Jacen needed to live, it was that the character named Anakin stepping into a "Chosen One" role was too close to the prequels, which were then in production. This is supported by multiple official sources:
Anakin and Jacen Anakin was supposed to be the series' hero and Luke's successor as leader of the Jedi. That would have been a nice counterpoint to Anakin Skywalker's rise and fall two generations before, but the plan was rejected. Among other things, Lucasfilm worried that it would be confusing to have the adventures of two different Anakins unfold at the same time. The result: Jacen and Anakin essentially switched roles.
Star Wars Insider issue 74, via Internet Archive
In the original story pitch, Jacen was the Solo child to die, killed by invaders who were certain he was the prophecied one who could be their undoing—when in actuality it was a reference to Anakin Solo. Feeling that it trod too closely to the beats being covered in the Prequel Trilogy, George Lucas requested that the prophecy be removed altogether and the central Solo changed from Anakin to Jacen, thus sparing Jacen's life but ensuring Anakin's demise.
The Essential Reader's Companion, page 390
Many have understood this to mean that Lucas specifically wanted Anakin Solo to die during the series, although Wookieepedia's article on Anakin Solo has purported quotes from Shelly Shapiro and Sue Rostoni from after the interview cited in the question, stating that that part of the storyline hadn't been an order from Lucas:
*Later, Shelly Shapiro clarified in the VIP thread in the official site that "Actually I don't really know what happened, I thought Lucas was involved but I'm not sure, what I said was just speculation based on what I thought I knew." Sue Rostini also stated that George Lucas did not order Anakin to be killed off. "No, George did not tell us to kill Anakin. He didn't tell us to kill anybody. He approved the deaths of characters, in theory, then told us who we COULDN'T kill (i.e., Luke). The creative group decided the main story plot points (i.e., the deaths) and the author(s) created the action and situations."
From Wookieepedia endnotes. The VIP thread on the starwars.com forums was subscriber-only and not indexed by Internet Archive, so these quotes cannot be verified.
The direction of Jacen's later character arc seems to have been a creative decision made by Del Rey's story group only after the New Jedi Order series finished and the Legacy of the Force series was being planned. It's unclear whether Lucasfilm or George Lucas had any significant notes on the LotF storyline, since the only characters who die in the series originated in the Expanded Universe.