A 32-year-old woman with newly diagnosed systemic lupus erythematosus presents with dyspnea and chest pain. Arterial blood gas shows pH 7.48, PaCO₂ 28 mmHg, HCO₃⁻ 21 mEq/L, and PaO₂ 65 mmHg on room air. Which investigation is most appropriate to confirm the underlying acid-base disorder and identify its etiology?