A 35-year-old woman with a known history of systemic lupus erythematosus (SLE) presents with gross haematuria, proteinuria (2.5 g/day), and hypertension for 2 weeks. Serum creatinine is 1.8 mg/dL. Anti-dsDNA antibodies are strongly positive, and complement C3 and C4 levels are low. Which investigation is most appropriate to determine the class of lupus nephritis and guide treatment decisions?