The flight crew decided to discontinue their approach to Runway 27 at Sumburgh Airport because of weather ahead. As it established on a southerly heading the aircraft was struck by lightning. The commander made nose-up pitch inputs but perceived that the aircraft did not respond as expected. After reaching 4,000 ft amsl, the aircraft pitched nose-down to a minimum of 19° and the applicable maximum operating speed (Vmo) was exceeded by 80 KIAS with a peak descent rate of 9,500 ft/min. The aircraft started to climb after reaching a minimum height of 1,100 ft amsl. Recorded data showed that the autopilot had remained engaged, and the pilots’ nose-up pitch inputs were countered by the autopilot pitch trim function, which made a prolonged nose-down pitch trim input in an attempt to maintain its altitude-tracking function.