Actually not quite: http://www.themovieblog.com/2007/10/economics-of-the-movie-theater-where-the-money-goes-and-why-it-costs-us-so-much/

Its usually far under 50% for movies with good legs and large international presence. I would argue that toy, ad and video game licenses + VOD is still not enougfh for them to recoup the entire cost, but they will easily do by the time Episode 9 hits the theaters. Good investment never the less.

And taxes, and budget for marketing and distribution... OP does not know business.

All it cost was the soul of the franchise.

Why Aren't Star Wars Toys Selling As Well This Year?

...but something has caused retail orders to decrease by about 47 per cent from last year.

https://www.forbes.com/sites/lukethompson/2017/12/21/why-arent-star-wars-toys-selling-as-well-this-year/#70a7906854e5

They'll make back the investment just in time for franchise fatigue to set in.

Indeed it has. Those box office sales are a small fraction of the machine that is Star Wars.

Obviously that's not all profit but lucas arts definitely under sold themselves.

To consider the deal's profitability, you need to consider opportunity costs. For example:

It's possible that if Disney never purchased Lucasfilm, Disney would have released an original IP or Pixar/Disney/Marvel film in its slot, which could have been wildly successful and not come a 4 billion price tag. So to consider the profit, it is not just against the 4 billions cost, but also against what Disney would have done with 3 alternate releases (which for Disney is probably in the 500 million/film range.)

On the other hand, it's possible that if Disney never purchased Lucas Film that they would have put out another money loser like John Carter or The Lone Ranger, which badly damaged Disney's reputation at the time.

Its also possible if Disney didn't buy Lucas Film, Fox or someone else would have, and the Star Wars films would be competing with Disney's release windows.

Finally, it's possible that the DOJ will reject the Disney acquisition of Fox's Film studios, and that had Disney never purchased LucasFilm, the deal could have passed.

I agree. Google paid 2 billion for Youtube a decade ago when it was a much smaller entity than it is today.

While i do think it hasn't yet because you are taking into account production costs, it has been undoubtibly a good deal for them.

This money could've been Lucas' but he never wanted to go for it. With 1 good movie (rogue one) and an awful new trilogy they already recouped. Pretty crazy really.