In 1777, Antoine Lavoisier helped convince the scientific community that sulfur was a basic element, rather than a compound. How could he be sure about this?

While I have not been able to locate his specific experiment(s) to prove that theory, it was one of Lavoisier's strengths that he carefully carried out precisely measured experiments, which was a great advance for the time. He was a leader in rethinking "elements" from the classical earth, air, water, amd fire to the substances we know today, based on their ability to be decomposed and compounded. Identifying Sulphur as an element is simply noted in many references, like https://en.wikipedia.org/wiki/Antoine_Lavoisier, as one of his achievements.

He presented several memoirs to the French Royal Academy in 1777, reporting on multiple experiments and his interpretations. While not apparently readily available online (in English or French), the Academy's successor https://en.wikipedia.org/wiki/French_Academy_of_Sciences likely still has these records.