It is my view that they level of criminal and treasonable activity in which both Willie and Hillie were and are involved is beyond belief. From Willie's days in Moscow and Hillie's flirtation will Alinski, both have worked against America and been well paid for doing so. Then Willie started to get Iraqi oil voucher money to add to the money he got from drugs while in Arkansas.
He has at least two obvious strategies, first, destroy paper/witness trails and second, create diversions. Monica may well have been intentionally developed as a diversion to shift attention from Vince's murder which would have lead to... whatever.
Willie is too smart to lie for the sake of lying. He lies to cover something other than the obvious.
He had to write something to collect his advance. As you say, he chose to lie about such matters because it was inadvisable to lie about other matters, like Chinese treason, the rape of Juanita Broaddrick, or the murder of Ron Brown.
This way he has people going over the same old ground: Lewinsky, Jennifer Flowers, and so forth.
He is also pathological liar, he does lie gratuitously, but he is very good at setting up smokescreens and distracting attention from one crime by committing another.