No really. There is a civil war already. Helping out a legitimate government is a good thing, if you can find one. Just ignoring it and hoping for the best isn't a great strategy either.
And now that "legitimate government" is collaborating with a foreign invasion, and owes a huge debt to the foreigners who put it in power for the explicit purpose of exploiting the country's natural resources.
Maybe I was wrong and the civil war is over, it probably doesn't need invasion but would benefit from a strong European partner to help develop the country. Libya should be a rich country. Ideally it would develop to the benefit of its citizens and Europeans who are looking for gas suppliers.
Will it still be seen as "legitimate"?