If a question asks you to react lithium (solid) and water (liquid). How do you know what the products will be?

In chemistry studies, chemical reactions should be classified into types, and you should memorize all types of reaction you have learned.

The reactants are lithium and water. Then, recall the type of reaction "reactive metal with water". You have learned the reaction of sodium or potassium with water.
2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g)
2K(s) + 2H₂O(l) → 2KOH(aq) + H₂(g)

All of lithium, sodium and potassium are Group I metals, and it can be deduced that lithium reacts with water in the same way of sodium or potassium. Very reactive metal (such as sodium or potassium) reacts with water to give the corresponding hydroxide solution and hydrogen gas. Hence, lithium reacts with water in the same way to give lithium hydroxide and hydrogen gas.
2Li(s) + 2H₂O(l) → 2LiOH(aq) + H₂(g)