。
She used to often be late for class.
Literal
[topic-は] often class [to-に] was-late [used-to-ものだった].
~たものだった is a variant of ~たものだ — the nostalgic-past construction, with the copula in past form (だった instead of だ). Both express 'used to' with a wistful or reminiscent tone; the past-copula version slightly amplifies the distance — as if the speaker is recalling an even more distant epoch. 授業 specifically denotes a class lesson session, distinct from 学校 (school as institution) or 講義 (lecture).