Does Lincoln MKZ hybrid 2011 model require synthetic oil?

Answer 1

No,

Per your owners manual (pg 314); In case you dont have a copy, I'm including a link below to see it or download it free online from Lincoln.

(Note 2)

"Use of synthetic or synthetic blend motor oil is not mandatory. Engine oil need only meet the requirements of Ford specification WSS-M2C930-A and the API Certification mark".

Reg or synthetic, its about the same price if you do it yourself (motorcraft 5w20 synthetic is less than $15 for a 5qt jug at Walmart). If you have it done at the dealership remember to ask for the "works fuel saver package" and you get the oil & filter changed, tires rotated, fluids topped off, and the Ford/Lincoln multi-point inspection, etc for $29 plus taxes. (Not endorsing, just telling you how to save a few bucks if you go this route. If I do it myself its about $20, if they do it and its about $12 more and they rotate the tires, top off fluids etc.)