"lying awake" is a correct and usable phrase in written English.
For example, you could use the phrase in a sentence such as: "After a long day at work, he found himself lying awake in bed, unable to rest."
The boy in Stratford, lying awake at night.
Eventually he was confined to bed, lying awake in torment.
For those lying awake worrying about money, meanwhile, one way out of their financial predicament might be to develop solutions for people lying awake worrying about money.
I remember lying awake in my dorm bed the first night I arrived on campus.
Keeping it going provides an excuse for lying awake in bed.
Life used to have natural pauses; standing in queues, riding the Tube, lying awake in bed.
That night, lying awake next to Caitlin, I tried to pick apart my feelings.
And you, fickle New York, where did you go after our nights lying awake together?
The boy in Stratford lying awake at night because of a story in a book.
Do his parents know he's lying awake, listening for his name?
And he quickly tired of lying awake nights wondering if the company was going to survive.
