Triple 13.5-inch turrets on the Lion-class hull

Could the Lion-class battlecruisers have been designed with triple turrets, and how much extra tonnage would they need?

Yes; the narrow 13.5-inch gun profile suggests a triple mounting could fit roughly where a twin 15-inch turret would, with only a modest beam increase.

Triple 13.5-inch turrets are plausible because the guns and mountings have a relatively narrow profile. A rough comparison suggests that a triple 13.5-inch arrangement could occupy space similar to a twin 15-inch turret, requiring only a limited increase in beam rather than an entirely new scale of ship.