Final answer:
Neil Peart joined Rush as the drummer and lyricist after the band's original formation. His complex lyrics and drumming skills played a crucial role in establishing Rush's reputation as an iconic progressive rock band.
Step-by-step explanation:
The drummer who joined Rush after its original formation and who is responsible for writing the majority of the band's lyrics is Neil Peart. Although not a founding member, Peart took over as the band's drummer early in their career, following the departure of the original drummer, John Rutsey. His virtuosic drumming skills and thought-provoking lyrics became a hallmark of Rush's sound and significantly contributed to their status as one of the most respected and influential progressive rock bands. Peart's lyrical contributions often draw on literature, philosophy, and his personal experiences, differentiating Rush's music with introspective and complex themes.