Lagiacrus seems to be a lot easier if you start by pumping him full of exhaust arrows: He won't have enough energy to spam his charges when he gets angry.
That's not how exhaust works.
Status effects work through hidden numbers. Every monster has a limit on the amount of status they can take. For the Lagiacrus, its limit is 180. When you apply the exhaust coating to your arrows, it increases that hidden status effect counter until it reaches 180, at which point, the Lagiacrus becomes exhausted. Signs of exhaustion are drooling, darkened eyes (Underwater monsters have glowy eyes that help you see them). Lagiacrus in particular almost immediately heads for land when it's exhausted. In any case, the exhaust status effect does nothing until Lagiacrus' limit of 180 is reached. IIRC, monsters can be pulled out of rage with the exhaust status effect, but they can't be exhausted and enraged at the same time.
Yeah, I know, it's not really intuitive.
EDIT: Now that I look back at the damage formulas for Tri, it's saying that when the exhaust tolerance limit is reached, they lose a large chunk of stamina. Well, I could be wrong, but I'm around 75-80% sure this is how it works because when I use a hammer, the monsters usually come out of enraged mode far faster than they normally do.