Can taking Advil (ibuprofen) cause stevens-johnson syndrome?

Yes. Nsaids and antibiotics and anti-seizure medications are the most common causes of sjs.
Uncertain (too rare) Stevens johnson syndrome (toxic epidermal necrolysis) is a severe, sometimes fatal, allergic reaction. It occurs in about 2-4 people per 1 million people each year. About half of the cases have no known cause, more than a fourth of the cases are felt to be due to infections by viruses, mycoplasma, bacteria, etc... The remaining 20% or so of cases are believed related to a variety of medications.