Amount of Hydrated lime to alum will depend on water hardness / alkalinity. 2alum:1 h.lime is a general use rate. I've used alum in several hard water ponds without hydrated lime and got good results. It all depends on water chemistry in the pond. Many areas of the US have ponds with low alkalinity and are weakly buffered to changss in pH, thus the need for hydrated lime to stabilize the pH due to alum causing acidity in the pond water. Hardness in water resists the lowering of the pH.
For a little more information here is a portion of a fact sheet from Ohio State University.
Alum (aluminum sulfate)
Alum is the most effective material for clearing clay turbidity from a pond, often within a few hours. Application rates are typically 100-450 pounds per surface acre. As before, add 1/3-1/2 of the required amount, wait a day, and then determine if additional alum is required to increase transparency to about 18 inches. Application procedures are identical to those described for gypsum.
For alum, there is a very good reason to use the minimum amount necessary. After application, there is a chemical reaction that impacts the pH (acidity) of the water. The reaction produces small amounts of sulfuric acid which can decrease pH significantly in some waters to levels harmful to aquatic life.
Therefore, alkalinity and pH should be tested prior to application. Alkalinity should exceed 100 mg/l and pH should be greater than 7.0. If not, hydrated lime needs to be added simultaneously to buffer the effects of the acid produced by the alum addition. Application rate for lime is 50 pounds per acre-foot. It is wise to re-check alkalinity and pH repeatedly as more alum and lime is added. In situations where 400 pounds of alum may be needed, pH may begin to drop quickly even in waters where pH was initially deemed to be adequate for lesser additions. Hydrated lime also removes suspended clay, although not as effectively as alum.
Entire Fact Sheet.
http://ohioline.osu.edu/a-fact/0006.html 
