Thank feck you're not an aromatherapist. Or a herbal remedy practitioner either, as Lavender oil is not the first essential oil I'd use for the symptoms described. Lavender is primarily used for relaxation, settled sleep and de-stressing massages.
Depending on the type of cough she has, there are several herbal treatments that will help. Peppermint tea is very good at surpressing the cough reflex. Marshmallow root, frequently used in commercially available cough medicines, is helpful in easing a dry, hacking cough. Wild Cherry Bark syrup is a great expectorant if she has a phlegmy, congested chest cough. A quick trip to Holland & Barratt by Paisley Piazza should sort her out.
If she wants to add an essential oil to the treatment, then Lavender can be used as it is a relaxant and inhalation will ease the respiratory tract. But I would recommend Cedarwood - good for loosening mucus, Eucalyptus - which does the same but with the added benefit of reducing inflammation. If she's been coughing that much, the throat will be very sore and Eucalyptus will ease that. She could also try Rosemary or Sandalwood oils - both of which ease upper respiratory tract infections.
Obviously it helps if she has an essential oil burner and knows how to use it! I am waiving my usual consultation fee as a favour to Mountain Ash and shall send some positive energies her way.
I realise you were trying to take the piss, (chanting any invocations to whatever deity would only exacerbate the cough, BTW, ya daftie!), but don't dabble in what you don't know. I wouldn't dream of advising you or anyone else of the comparative benefits of Monster Munch over Quavers, for example.
Blessed Be! )O(