It depends very much in which region you are investigating. In regions with lakes of icing certainly the water temperature is not going lower than 0 (when lake is salty can be also cooler, but not much). Thus, anyhow your air temperature can be -10 C, the water temperature will not go down, but if lake is too shallow it starts freezing and then relation disappears at all.
Thus, climatic region is very important.
Second, the depth of lake. In both hot and cold regions, the amount of heat to absorbable in water depends very much on depth of water body.
Thus, these points mentioned does not allow to have relation between air and water temperature suitable for all lakes in all climate regions and independently from the depth of lake.
Thus, can you ask more precisely? Which lakes and where you are investigating?
Thanks for your contribution, my case is in Iran and its name is Urmia Lake. It's about superficial one of approximately 11 m depth and is world third saline lake. The climatic meteorology of the region is of cold-arid mountainous division.
Beside modeling of the energy budget of the interface water-atmosphere for which you will also need meteorological data the simple empirical way is to conduct measurements of both water and air temperatures for enough long period in order to include extremes. Then you may use any statistical software to fit an equation. The third way is by using the analogy with an already studied case having similar climatology.
Of course, for the time being i have just climatic data of the region and need for those data for that region water temperature. I require the obtained relation having the same meteorological situation.