"a lot of leeway" is correct and usable in written English. It is normally used to refer to a situation in which someone has a lot of freedom to do something without facing too many consequences or restrictions. For example: "In their research, scientists are given a lot of leeway to explore new ideas.".
"We give him a lot of leeway in getting open.
"We just don't have a lot of leeway," Houston said.
So we're going to give him a lot of leeway".
Even though I work for a big corporation, my job still offers a lot of leeway.
Greer says that even for younger stars there is a lot of leeway.
"This gave him a lot of leeway in his conduct," Mr. Kirn writes dryly.
(Editors in those prerecording days had a lot of leeway to fix up presidential prose).
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com