Let's plug in a few figures to get a ball park idea on how this would all work. LCC being asset rich are able to borrow at a lower rate (has been said to be half) what a business could borrow at.
Let's say that's 2% versus 4% (seems about right from some quick searching). Let's also say the stadium costs £350,000,000. What does this mean over a 40 year loan?
At 2% you're repaying £12,700,000 annually. At 4% you're repaying £17,600,000 annually. That's a savings of £4,900,000 by borrowing through LCC. You're actually still making money on the deal after giving LCC their £4,000,000 fee.
Just on that basis alone this seems like a no-brainer to me, and there are also many other benefits in financing this way.