Chiromancy

[milo]

waking and then lay down again: lie would be a better choice.

"lie would be grammatically incorrect due to tense disagreement.

milo

lie: to be or to stay at rest in a horizontal position : be prostrate : rest, recline
lay: past of lie; to put or set down

laid: past and past participle of lay

If anything laid would fit also, correct?

laid would be grammatically incorrect. The poem takes place in the past. You have to use the past tense of the active verb "lie" which is "lay". Laid is past tense of "lay" which is a transitive verb. You can lay something down but you can never lay down, you can only lie down.