sleep: the natural rest in which a person lies still and unaware
At its heart the word names plain sleep, the nightly rest of the body. People wake from it (Jacob at Bethel, Samson in Delilah's lap), are robbed of it (Jacob during his hard years with Laban, a sleepless king, Nebuchadnezzar troubled by his dreams), or find it sweet (the tired laborer, the person who trusts God and lies down in peace).
From that plain sense the Hebrew builds two vivid pictures. Death is spoken of as a sleep from which no one wakes, a perpetual sleep. And the lazy person's ruin is shown beginning in bed: a little sleep, a little slumber, and then poverty arrives.
In every case the word itself still means sleep. The extra weight of death or of laziness comes from the surrounding verse, not from a second meaning hidden inside the word, which is why one meaning with a few shades covers the whole range.