Turns in battle are calculated differently and do not depend on morale. Strangely enough, a turn in Heroes 5 is a time interval between the actions of a creature with an initiative of 10. That is, a creature with an initiative of 10 will perform 10 actions in 10 game turns, while a creature with an initiative of 12 will perform 12 actions in the same 10 game turns. Therefore, the higher the initiative, the more often the creature will take its turn. Those who understand the game mechanics will understand me.
In short, feel free to take the Lion's Necklace and other items that increase morale into battle; this won't make invisibility end faster, it will just mean that your stalkers will get to take their turn more often. (Don't forget to increase my morale)