hii and thank you for the question! :3

while they don't have big arguments, leona and lizzie get a bit riled up when the other is being unfair to themselves.

for lizzie that's leona's depression ruts in which he typically loses hope and devalues his impressions on people, or when he's having intrusive thoughts or nightmares about his unique magic and is being stubborn about accepting that people do like him and that he is meaningful.

for leona it's how lizzie clings to her ex and blames herself for his death. to leona he's just an ass who got what he deserved, for lizzie he's her beloved childhood friend who inspired her to go on land in the first place.

they never argue for long and usually manage to comfort each other though, so all is well :D