Intricate and lucid are not opposites, so I wouldn't expect them to be in each other's antonym list.
Lax is an antonym of prim, especially when not stiff or not precise is the implied meaning. Lax is also an antonym of tenacious, when the implied meaning is not persistent. Prim and tenacious are not synonyms, as you pointed out, but the respective opposites that I listed are synonyms of the word lax. In other words, prim and tenacious can share a common antonym. This is not unusual.
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