you should try to follow the lecture without asking questions unless you ... something important.
A, would miss
B, have missed
C, will miss
D, had missed

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I'd say A or B, leaning slightly more towards B.
A sounds like you shouldn't ask questions unless that has the possibility of you missing something important, which makes sense
B sounds like you shouldn't ask questions until you miss something, which makes sense
C sounds weird to me because you don't know if you've missed something important until it's said, if that makes sense? So you don't know if you need to ask a question until AFTER the thing you've missed has been said
D sounds weird because the rest of the sentence is in present tense