De Broglie's relation
is a very old and mostly outdated concept. Nowadays nobody uses it for anything. De Broglie's theory was soon superseded by Schrödinger's theory, and people only use the former as a teaching aid in schools. The range of applicability of de Broglie's theory was very limited when it was proposed, and today we only study it because of its historical relevance, as it laid down the foundations of QM in general, and wave mechanics in particular.
Nowadays, de Broglie's relation is regarded as a definition of $\lambda$,
and as such, is just as valid in SR as it is in GR. On its own, it is devoid of physics. In any case, it is not derived in the framework of special relativity, because it is not a derived relation. It's just a definition.