These lineups demonstrate minimal reliance on technology cores and can be used in every match in Teamfight Tactics.
Irelia and Her Allies
If you didn't know, the Irelia and her Allies lineup operates similarly to the Idol strategy combining Kai'Sa, Akali, Viktor... in the first half of Season 6. Essentially, you still play around a single carry unit and buff it immensely thanks to the Idol effect. The strength of the Irelia and her Allies team in Teamfight Tactics Season 6.5 is that this unit costs only 4 gold and is easier to upgrade to 2-star compared to 5-gold champions.

Furthermore, the Idol trait itself includes Gnar and activating the 2 Attack milestone with Irelia is incredibly easy. Consequently, all you need is a well-equipped Irelia and a 3-star Idol milestone to comfortably climb the ranks. So, no matter how flawed your technology core is, as long as it adds attack, defense stats, or provides some form of energy regeneration for Irelia, it's a viable choice.
Renata - The Warrior
Renata - The Warrior: Exemplar of Dominant Lineups Independent of Technology Cores

The Renata - The Warrior lineup epitomizes the use of powerful champions, rendering technology cores irrelevant. This lineup utilizes durable Warrior units with high health pools and the Vanguard effect, capable of withstanding tremendous damage without needing support cores. Additionally, the two carries of this lineup - Renata and Viktor - do not synergize well with Scholar or Sorcerer cores as they can deal significant damage without activating their respective traits.
Draven - The Elegant
Although employing a vastly different set of champions and lineup, Draven - The Elegant operates similarly to the Irelia-centric composition. Essentially, you must do everything possible to empower your carry, in this case, Draven, to deal maximum damage. Unlike Irelia, Draven already has long-range attacks, even infinite as a VIP, so this unit doesn't require defensive or healing items to safely deal damage.

Therefore, when operating this lineup, the most important thing is to upgrade Draven and equip him with the necessary items for disruption. You can even choose technology cores that provide items or upgrade Pandora's Box to obtain the best equipment for Draven. Even if you don't have any cores that directly upgrade the Elegant race, as long as Draven is well-equipped, this unit can easily carry the team.
