Post History

You are right, "raise (someone) out of trouble" is not a common English idiom.  It is used to connect the English meaning (denotation and connotations) to the original Latin and/or Old French meanings (denotation and connotation).

The bolded phrase is an explanation of a notion operating in Latin, in Old French, and likely to be discernible to many speakers of Middle English, too.  The notion is generally obscured or absent in Modern English "relieve".

Nevertheless, let me elaborate on what Etymonline means by "raise (someone) out of trouble" in that particular context.

When a person is "in trouble", they are not literally surrounded by trouble, they are only figuratively "in" the trouble.  Equally figuratively they could be "raised", or equally figuratively "removed" (moved) to some less troublesome circumstances by a powerful force or authority that is capable to change that person's circumstances enough so that they are no longer "in trouble".  See the Etymonline text following your bolded sentence for some attested examples where the troublesome circumstances are a mediaeval battle.

I don't know how the presumed spatial metaphor is supposed to apply in Modern English, but it's perhaps irrelevant if you can appreciate the explanation which Etymonline gives for Latin - namely, that a heavy burden is taken off the person, making them lighter/lifted up/escape the burden upwards).