I'm sorry to hear of this with Sphinx. I'm sorry that your question wasn't answered in a timely manner. Her thunderstorm phobia can be addressed medically or by behavioral modification. Zoetis has released Sileo - a product containing the dissociative drug dexmedetomidine - for addressing noise phobias. We ordinarily use this drug to induce a "spaced-out" state in which our patient doesn't care what's going on around him/her thus allowing us to perform medical procedures that wouldn't be allowed otherwise. At lower doses, Zoetis found it to be effective for noise phobias as well. Sphinx's vet can prescribe this drug for Sphinx.
Many noise phobias can be managed successfully with behavioral modification. The prognosis varies greatly depending on the individual, the duration of the phobia, the ability to control strong stimuli during treatment, and the success in finding an effective, controllable artificial stimulus to use during exposure exercises.
Successful treatment of thunderstorm phobias using only behavioral modification can be very difficult because of the presence of multiple stimuli, difficulty producing an effective artificial storm for desensitization, and inability to control naturally occurring stimuli during therapy.
If you're home with Sphinx when a mild storm occurs, it may be helpful to distract her and then have a "thunderstorm party". When she begins to show mild anxiety, you should ignore her and make an unusual noise (squeaker, whistle, tap table top, crinkle paper, clicker, e.g.) so he orients to the new sound and stops acting anxious. After about 10 seconds or more, but before she begins acting anxious again, you should jump up, run to the kitchen, and grab a handful of meat or cheese treats. Next, you should run through the house acting very animated, saying happy things loudly in an upbeat tone and tossing food about for Sphinx to eat. Unless the storm becomes strong enough to make her fearful and take her focus away from you and the food, the "party" will serve as a counterconditioning session.
(There are older anxiolytic drugs as well. The benzodiazepines (alprazolam, chlorazepam, lorazepam, e.g.) and tricyclic antidepressants (e.g. clomipramine and amitriptyline) may be helpful for difficult cases. The benzodiazepines are the best choice to use on an as-needed basis, and alprazolam (Xanax) may prove to be the most potent for panic-type responses, although its duration of effect may only be a couple of hours. Tricyclic antidepressants may take several weeks or more to become effective and are probably best reserved for chronic problems. A dose of benzodiazepine may also be added to the tricyclics on an as-needed bases an hour or two before a storm is expected. Other options are the use of D.A.P. (Adaptil/Dog Appeasing Pheromone), buspirone, or a phenothiazine tranquilizer (Acepromazine) given 1-3 hours prior to an anticipated storm (which doesn't reduce anxiety but may be sufficiently sedating to avoid the problem entirely).)
Please respond with further questions or concerns if you wish.