Apply the (1/2) multiplier to the paladin level only. Your example paladin can use Lay on Hands 6 times per day.
This is consistent with mathematical order of operations; in
0.5 * <paladin level> + <CHA>, you only apply the multiplication to the paladin level. In order to indicate an equation such as
0.5 * (<paladin level> + <CHA>), It should be worded "a number of times equal to 1/2 the sum of her paladin level plus her Charisma modifier", to emphasize the grouping.
This also fits with other class abilities, such as the cleric's channel energy ability: "A cleric may channel energy a number of times per day equal to 3 + her Charisma modifier." There are many such abilities that add an ability score modifier to another number (often based on class level). In the case of Lay on Hands, the "other number" is 1/2 paladin level.