Actually they are very similar, they both are about the humanitarian precedent
In Libya the West intervened initially because of the Siege of Misrata
https://en.wikipedia.org/wiki/Battle_of_Misrata
That was the catalyst and it should be an easy sale to understand that Western intervention in the beginning of the Syrian conflict and assisting to remove Assad cannot be seen as a bad thing if you look at the reality of Syria now
And I'm not suggesting for a second that there arent other factors that influence the West but we cannot ignore the humanitarian aspect
Not quite sure sanctions is akin to airstrikes and funneling arms to rebels in an attempt to change a regime just because you dislike them, nor is intervening to stop a verified mass slaughter of people (heh, in practice this is when you dislike a regime, I suppose).
How can we look at Syria and the rise of ISIS and figure this wasn't a bad idea. As for Misrata, well, those rebels started a war.