"The boss asked he do not be lazy with his work" "I insist he do not come late to the meeting" I don't hear the versions with "do," but they're probably correct. Surely, in a "that" clause, the "do" is optional: I ask that you [do] not reveal the source. Without the negative, "The boss insisted he do be on time" seems perfectly natural.
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GuyperA."The boss asked he not be lazy with his work"I don't hear the versions with "do," but they're probably correct.
"I insist he not come late to the meeting"
B."The boss asked he do not be lazy with his work"
"I insist he do not come late to the meeting"