The limiting reagent is the LiOH. There is 1 mole of excess HBr. 1 mole of LiBr and 1 mole of water will be produced by this reaction.
This problem can be solved by interpreting the balanced equation. Because there are no coefficients, we know the reactants and products have a 1:1:1:1 ratio.
This means that to allow the 1 mole of LiOH to fully react, you will need 2 moles of HBr. By subtraction you can calculate that there is 1 mole of HBr which will not react (leftover).
Because there is 1 mole LiOH which limits how much of the products will form, you can conclude that there will be 1 mole of each product formed.
Here is a video lesson describing a technique you can use to determine limiting and excess reactants.