To Lizard Squad, their DDoS represented a strong and clear message to Sony and Microsoft telling them to upgrade their servers for online games. But to all of the people that wanted to play their new video games on Christmas, it was the ultimate "fuck you, go spend time with your family, you loser".
The Lizard Squad has publicly expressed their concern not for both companies charging customers for online services, but for the vulnerability of these servers and how commonly they are targeted for problems and outside attacks (the irony, it burns). Their message of a DDoS expresses this by effectively ruining the chance to start playing online with new games by blocking out server availability. They say the attack has lasted between 12 to 14 hours, and are ashamed by the dependence players have to their consoles.
In interviews with Lizard Squad Members (according to playstationstyle.net), the members had no regrets or second thoughts for their actions, and don't have fear of having legal action taken against them for the attacks, claiming it to be a "win-win" for them.
The attack was a rather vague one, as there was a lot of confusion around what was causing the attack. It was assumed that terrorist groups related with North Korea did it to PSN in retaliation to Sony's making of "The Interview", a movie starring Seth Rogen, revolving around a plot to assassinate of the current dictator in the country, Kim Jong-Un, during an interview. The production of the movie was released with major controversy, including the threat of terrorist attacks to theaters attempting to air the film itself. Coincidentally, the movie was released on Christmas day, the start of the DDoS by Lizard Squad; it is unknown if their attacks were influenced by Sony's production of the film.
And in the end, PC gamers are still having shits and giggles with their pointless PC Master Race, laughing at how it's only PSN and Xbox Live that get attacked.