Gaddafi was under sanctions a long time, and he buckled under those not Bush's invasion. He had already begun to negotiate an end to the sanctions and reparations of Lockerbie before Iraq, though it's not surprising Bush would try to rip off the credit for it anyway.

As to scaring Gaddafi it may well have done, though it seems unlikely to be more than a suck up. At no time did Bush suggest invading Libya nor was it in the Axis of Evil. So it's hard to see what Gaddafi was frightened of. If at some stage in the future threats were made against Libya then credit could be taken for the effects of those.

It may even be that Libya was threatened secretly but a man who resisted Reagan and the sanctions would be so easily scared has no evidence at all to support it. Then again Bush usually does everything with little or no evidence to support it. Bush may deserve some credit but his trying to steal all the credit is just dishonest.