Word meaning a certain phrase?

Well, "restless" can be used to describe someone who can't sleep so "I lay restless in bed but longing for sleep" could work or something similar to that such as "I lay in bed but the sleep I seek is out of reach". I hope this was helpful!

A few thoughts: words like sleepless and wakefulness, both describe an inability to sleep by one who desires sleep, though neither describes or requires being in bed at the time.

However, one who desires to sleep but is unable whilst laying in bed is often said to be, tossing and turning.

toss and turn: to move about and turn over in bed because one is unable to sleep (Websters)

Insomnia describes the first part: "I want to sleep more, but I can't" but not the second: "so I'm laying in bed." It can also name it as a geberal patrern, say over several weeks or as a medical condition.