If you’re talking missing lore you can just do the interference mission and when you talk to Eris at the end just keep hitting the talk to Eris button until the lore you’re missing pops up. I missed a week and that’s how I got it.
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You don't need the lore for Forerunner, you need to have done the three different rotating missions. Someone in my clan is in the same boat, between being forced out of his house because of work and then getting a bad run of luck on what missions have actually been rotating in, he's missing exactly one encounter for the entire title, just like OP.
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Tbh I didn’t even pay attention to forerunner until last week and when I did look all I had left to do on it was shoot the eyes, so I didn’t bother looking at the other requirements since I did them without knowing already. I missed a week doing interference and still got it