I'm preface this by saying I've never done this but I do have lots of experience washing lighter oils with water.
You can use as much vinegar as you want as long as you was it out. Since vinegar is an acid, if any is left in the fats then it will nuetralize some of your lye. Simply change the vinegar/water after you've deodorized the fats with straight water, agitate and allow to settle.
Personally, I'd try baking soda first.
The technical soap manuals from the late 1800's would suggest you melt the fats and mix with salt. This dries the fats and coagulates the "other" materials. Allow to cool, take the fat layer off the top and reheat and mix with fullers earth. This will deodorize and lighten the color. You then have to filter out the fullers earth though. I never found a specification for what filter size is needed...