Luck played a part for sure, but not the most important part. They are clearly more motivated than every other club in the Champions League. No matter what they do in the other competitions, they almost always show up in CL. Other teams are not able to do that, swtich on like that. If they are not playing very well in the league, they will not play very well in CL either.
This is how they have managed to win many CLs without necessarily being very dominant as a whole. They can win multiple CLs while not being the best team in the world, while being 3rd or even lower in La Liga. It's a skill, and Madrid in CL have it.
This is the first time they win CL + League, which is the sign of a possible dominant era for them.
I think the real reason why Madrid is dominating Europe is b.c they have the best team in the world. When I say the best team, I don't only mean their starting 11 (Which madrid never really had one), but also their bench players . If Cristiano and Bale and Benzema were struggling, they had other players who showed up. Isco, James, Asensio are among those player madrid could rely on,even morata at times. Real Madrid has the best bench in the world. They have players in their bench that could easily make it into their starting 11 and also ours, players like Asensio which I believe to be better than our, unfortunately, old Iniesta. In modern football, with so many games and competitions, having more than 11 players that can make a difference is what counts. With so many injuries, bad spells, tiredness, etc, having players that can come from the bench and be just as good as the ones playing is what sets Madrid from every other team. In other words, Madrid is the richest club in the world and finally understand that having 22 quality players is better than having 11. Also, Barcelona taught Perez ( madrid's president) that is best to try to sign the best spanish players instead of trying to sign players from other countries. There is no spanish players that could say No to Madrid, even Isco, a barcelona fan couldn't resist the amount of money Madrid were gonna offer him.
To summarize: Madrid have the best bench in Europe ( and probably the first or second best 11)
Madrid doesn't suffer when one of their top players ( Bale) gets injured b.c they have so many quality players to replace him with.
Madrid has signed the top spanish talent coming up ( Asensio, Isco, now they are after Theo hernandez whom I believe will be the best left back in spain in a couple years. Yes, I know that Theo Hernandez is french, but in the last few days there have been rumors that he has chosen to play for spain instead .