'a lot of freedom' is correct and usable in written English. You could use this phrase in a variety of contexts. For example, "Having a job overseas gave me a lot of freedom."
"We have a lot of freedom now".
"We had a lot of freedom".
It gives me a lot of freedom.
But we had a lot of freedom.
I gave him a lot of freedom".
With poetry there's a lot of freedom".
He says that Mourinho gives him a lot of freedom.
From then on, it was a lot of freedom".
"Dwight will give Kobe a lot of freedom defensively.
That's a lot of freedom for one video game.
"You have a lot of freedom," he explains.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union