I'm confused by these sentences.

Question

Confused by the use of "Lui" in "je LUI ai fait faire sa valise" and "je LUI ai même bandé les yeux" as they both don't use "à"? Or am I mistaken?

Accepted Answer

Hi James, 
Just to add to the other answers.
The indirect pronoun 'lui' replaces the whole
à + person
Take a look at the following Kwiziq lesson for more explanation -
Replacing people with lui, leur = him, her, them (indirect object pronouns)
Bonne Continuation!

Answer

Hi James,"Je lui ai fait faire sa valise."  I see this as a "faire causative" construction where the subject has the suitcases packed, not by the subject but by an agent on behalf of the subject (him or her) -- "I have had the suitcases packed by him/her""Je lui ai même bandé les yeux" --> "I even blindfolded her/him" (the eyes of him/her)In each case above lui is the indirect object 1) the agent of the action 2) the owner of the eyes.Hope this helps.Jim

Answer

Just to add to Jim's answer:
You can better see the construction if you substitute a specific person for the indirect object pronoun lui:
J'ai fait faire ma valise à mon frère. -- I made my brother pack my suitcase.Je lui ai fait faire ma valise. -- I made him pack my suitcase.
Here it becomes apparent that lui replaces à mon frère.