Not necessary, because the argument concerns only the effects of inhaling lavender. Whether other scents that reduce susceptibility to illness do so by reducing stress has no impact, because we already know from the premises that inhaling the scent of lavender does reduce susceptibility to illness in part by reducing stress.

Necessary, because if this were not true — if NO people who regularly inhale the scent of lavender would otherwise be under enough stress to impair their immune systems — then we have no reason from the premises to think that the practice of regularly inhaling the scent of lavender is helping to protect those people from illness. Even if they weren’t inhaling lavender scent, the immune systems wouldn’t be impaired by stress. So they wouldn’t benefit from the stress-reducing properties of inhaling lavender.

Not necessary, because what matters is whether inhaling the scent of lavender can reduce the illnesses of people who regularly inhale the scent. Whether those people are more vulnerable to illness than the average person doesn’t prevent them from experiencing a reduction in their own incidence of illness due to inhaling lavender scent.

Not necessary, because even if for some people who inhale lavender scent, the way the scent reduces vulnerability to illness is mainly through some other method besides reducing stress, that’s consistent with the author’s reasoning. The author never concluded that there’s no other potential way for inhaling lavender scent to reduce vulnerability.

Not necessary, because even if reduced stress lowers vulnerability to illness for other people in addition to those who are under enough stress to impair immune systems, people who regularly inhale lavender scent can still be among the people for whom reduced stress reduces vulnerability to illness. Although the author assumes that those people have immune systems that are impaired by stress, these people don’t have to be the only kinds of people who benefit from inhaling lavender scent.