The R2P is a slogan that has some media efficacy but a rather dubious legal existence. That does not prevent the majority of observers asserting that it was the basis of Resolution 1973, authorizing intervention in Libya. That is not true either. The Resolution reiterated the internal responsibility “of the Libyan authorities to protect the Libyan population”, but nowhere did it speak of an external responsibility of the international community to intervene. This does not imply that the concept did not play a role in the motivations of certain permanent members, only that it is not considered as a consensual “norm” worthy of being explicitly mentioned.
The military intervention in Libya did not represent an implementation of a purportedly universal “responsibility to protect”, but an ad hoc consensus among powerful states. Moreover, it was motivated by both humanitarian reasons and national interests, as British Prime Minister David Cameron explained in his March 18 speeches evoking the security risk for Europe, posed by terrorist threats and potential migration pressure. It is also a question of moral image and political gain. Nicolas Sarkozy used the intervention to consolidate his presidential calibre and keep the failures of French diplomacy in Tunisia and Egypt out of the limelight.
I definitely agree that the intervention was an ad-hoc arrangement where a combination of principles, interests, and opportunities facilitated intervention, but I’ll leave the rest to international-law scholars.