His battle anger is not actually anger. Its more intense focus. He seems frustrated or annoyed but its just how he acts in battle to give off a more commanding presence. You'll know he's fine if he smiles when yelling a command or he moves his cloak in a dramatic fashion (we've seen the Gen 4/let's go sprites we know he got some drama in him)

Lance's ACTUALL temper comes out a little different.

His anger comes out in one of two ways: 1) Silent brooding stare. This is his most common form of frustration - usually towards someone else's attitude, something going wrong for him, or listening to someone talk about team rocket for the thousandth time. He’s annoyed but still in control of himself.

2) Pure unadulterated rage. This is rare for him. Lance only loses control of himself under VERY specific situations. Someone directly harms a pokemon in front of him, someone harms someone close to him. Either of those and he will go off. Whether it's physical violence or a pokemon battle, you will know he’s lost it.

When he’s bad, constantly balled up fists, poor man has nail imprints in his pams from how hard he clenches his fists. His face is the biggest tell. He won’t go red in the face (His hair does that already) But his eyes give it all away. Dark and focused, almost vacant to anything else around him other than his target.

He LOCKS ON

We all saw how he handles team rocket, same stare, that pure focus and commanding presence is the exact same as when he loses it fully.

Now let me make this clear, he talks a lot and he is honest. He will say exactly what he means but he will try and be polite and not offend on purpose. Unless he's frustrated:

Lance will speak A LOT less when upset but when he does, he will make whoever his anger is target at, feel as small as a Tynamo. He will never do this to someone he cares for however. He will simply leave the room and take his frustrations out on a random tree before coming back.

Whilst he is passionate he will never hurt someone he truly cares for, it would go against everything he's worked to protect.

Although he is incredibly easy to calm down. Again i must specify he IS IN CONTROL he doesn’t need anger management therapy for problems of acting out, no his is a calm man with a strong moral compass so when he defends something or someone he will go to hell and back.

To get him to calm down, if he is brooding, just take him away from the situation and talk to him about something he likes, usually enough to calm him down. If he’s locked in however, that is leave him alone and let him pace around. Remove him from whatevers getting him ready to punch someone and just let his pokemon calm him down. 

If you know Steven Universe, how ruby paces around when upset. Same thing just minus the speaking, man has an inner monologue with himself.