'a lot of play' is correct and usable in written English. You can use it to describe a situation where a person or group is doing something for a period of time, usually for enjoyment. For example, "There was a lot of play at the park today as the children enjoyed the nice weather.".
There's been a lot of play in making the piece.
The story garnered quite a lot of play.
A lot of play in Sweden's zone early on.
It became a product with a lot of play value".
"Curly hair is like redheads -- they just don't get a lot of play," Ms. Stanger added.
Many Washington insiders watch the poll closely, so expect it to get a lot of play.
"Currently, game development relies on a lot of play-testing to determine where to place these types of items, and such play-testing doesn't always get things right".
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia