The phrase “a lot of stress” is correct and is often used in written English. You can use it when you want to emphasize a large amount of stress. Example: The report was due in two days, so I was under a lot of stress to get it done on time.
A lot of stress?
I had a lot of stress.
It is a lot of stress.
Better not a lot of stress.
"But it removes a lot of stress".
That caused a lot of stress.
It relieved a lot of stress".
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia