The obvious use of Last Stand is to make Nene not die when she otherwise would, such as by taking massive damage from arts with long windups. The aura lasts long enough that timing it isn't too strict, but it does still have to be timed, or it will be lost - and its cooldown is long enough that it'll be a long time before she gets another chance.
A less-obvious use is to intentionally let Nene's HP drain so she can use the aura and benefit from its healing, allowing the party to spend their healing arts elsewhere or wait for them to recharge. This sounds counterintuitive, but why heal Nene for 25% when you can let her heal herself for 50% first?