No, you don't require anything from Fable II's DLC for Fable III. The only thing that will pass to Fable III will be your final Fable II choice that will eventually apply little changes in your Albion. (such as a zone is richer or poor and such minimalistic changes)
However, Fable II's DLC's are good and provide a certain degree of fun, also if you have lost your faithful companion you may bring your dog back to life with Knothole Island DLC.
This depends on every person and Fable II player, to be honest. Therefore, you should check them out fourthly yourself using various review sites and/or youtube videos, which will give you an idea of what the DLCs really give you, a Fable II player as an additional experience to the game.