Lattice Energy (enthalpy) I know that when making a bond the reaction is exothermic (positive)
and breaking a bond the reaction is endothermic (negative).

Lattice enthalpy or lattice formation enthalpy is defined as the enthalpy of formation of 1 mole of an ionic compound from gaseous ions under standard conditions, which is endothermic (negative).

My question is ..
Why lattice formation is negative? It should be positive when making the ionic lattice because we are releasing energy.

Is bond making/breaking different than lattice making/breaking?
You have to consider the system. If energy is being added to the system the sign is positive, if energy leaves the system the sign is negative.