There's some ambiguity in the sentence, and this seems to be causing the grammar checker to misparse it.
The intended parse is
It’s not our (lack of (answers to these problems)) that causes us such pain.
"lack of XXX" is a singular subject, so a singular verb is appropriate.
But I think it's parsing it as
It’s not our lack of (answers to these (problems that causes us such pain)).
In this case, "problems" is the subject of the last clause, so a plural verb would be appropriate.
It could be even a simpler mistake, it may just scan back to the closest noun, and assume that's the subject of the verb. Parsing English is hard, especially with nested clauses and prepositional phrases.