Could I trouble you to arrange for a lawyer?

Literal

Lawyer [obj-を] honorable-arrangement can-receive-not (polite)?

A very polite request. お世話 means 'assistance, arrangement, taking care of'; 願う is 'to request,' and 願えませんか is its potential negative question form ('couldn't I receive...?') — the double softening (potential + negative question) is a canonical polite-request move. The お~願う pattern is a productive humble-request frame: お返事願う ('request a reply'), ご連絡願う ('request contact').