Adam Clarke on John 11:12

If he sleep, he shall do well - That is, if he sleep only, etc. Though the word sleep frequently meant death, (see Act 7:60; 1Cor 11:30; 1Cor 15:18, 1Cor 15:20), yet, as it was an ambiguous term, the disciples appear here to have mistaken its meaning. Because, in certain acute disorders, the composing the patient to rest was a favorable sign; therefore the words, If he sleep, he shall do well, or recover, became a proverbial forth of speech among the Jews. In most diseases, sleep is a very favorable prognostic: hence that saying of Menander: - Ὑπνος δε πασης εϚιν ὑγιεια νοσου.

Sleep is a remedy for every disease.

See Grotius here. The meaning of the disciples seems to have been this: There can be no need for thee to go into Judea to awake our friend Lazarus; he will awake time enough, and his very sleep is a presage of his recovery: therefore do not hazard thy life by going.