Please dont follow the old books for order of reactivity series. Follow the new edition books and all books will have same reactivity series. But most books only give the reactivity order of some important elements. But some books have a couple of more elements added to this. This may be the reason you felt so.
It is always considered that Potassium is more reactive than Lithium. Mainly because as atomic size is larger in Potassium, the nucleus has lesser effect on the valence electron and thus can give it away more readily than Lithium. You will learn to explain this with the concept of ionization energy in class 11. That is, Potassium is much more reactive due to lower ionization energy due to larger size.
There is no unique and fully consistent way to define the Reactivity Series, but it is common to use the three types of reaction- 1) Reaction with Water 2) Acids, 3) Single Displacement Reaction. The most reactive metals react with water easily then in middle of series the metals react with acids n then comes how easily one metal can replace other in simple displacement reaction.
You will come to know much more about these things in class 11 with much more chemical reactions and mechanisms.