Modern airliners are designed to be able to withstand the worst (vertical) turbulence. But what about the rarer lateral (horizontal) turbulence?
Yes they are.  FAR 25.427 has the requirements for lateral gust loads.
I don't know if there was FDR information for the BOAC flight, but it may very well have been a similar event to AA Flight 587, the one that lost its vertical fin over NYC when the pilot got on the pedals in reaction to a wake turbulence encounter that induced a large yaw, and made rudder input loads that the fin is not designed to handle.
In that case the fin broke off not because of the gust, but because of the control response.  You will likely be out of phase in the attempt, and your inputs become &quot;doublets&quot;; amplifying inputs that make the yawing worse.  You don't normally touch the rudder pedals on an airliner between departure and landing unless an engine quits; you just let the yaw damper take care of yaw excursions like that and it'll have no problem staying in phase to dampen the motion.  I'll bet that the BOAC incident was that sort of case, where a gust reaction was followed by an input, at high speed.