Why does the water in the recipe for dough making not have a definite temperature or an advise about temperature?

The recipes lists 60 cc of milk and specifies 25 C in Summer and 45 C in Winter but for 150 mL of water it merely says lukewarm water. The recipe is in Japanese but I can understand it. The recipe is for wholemeal bread. It uses 9g of yeast and 150 g each of wholewheat flour and self-raising flour. It says to mix the dry ingredients and then add the milk and water slowly.

It doesn't have definite temperature because you don't need it. The dough will work with any temperature water you use, anywhere between 0 and 40 C. The difference will be in the time needed for the dough to rise, and the amount needed kneading to get the same gluten strength. But as these parameters are not firm, but you proof until the dough is risen properly, and knead until it is kneaded properly, you don't have to start with a specific temperature.

You don't need it for the milk either. But if the recipe author wants to spend roughly the same time preparing the bread, they must have used this temperature to achieve similar rising times for dough left to rise at room temperature, or maybe yeast left to proof at room temperature as suse mentions in a comment. It is just an additional convenience which can be followed, but is optional. So there is no need to supply it for the water either.