[]What logic connection is there between 1. and 5. ?
There is no etymological connection between the two. Before becoming homonyms, the verbs were different in Old English: (1) licgan and (5) léogan. [/]
Now this is interesting: [:"red"] licgan and léogan [/]became lie down and lie in English.
In Dutch lie and lie is : [:"red"] liggen and liegen[/]. As you see the Dutch words have stayed closer the Old English ones than the New English words.
Now I must guess that licgan became liggen . And léogan became liegen . I like that. (and will just go on making mistakes)
liggen = lie down
liegen = tell a lie
It could be easily argued that to tell an untruth is putting aside (lying or laying down) the facts.