You could but generally the norm is the accused demands a trial by combat. Only reference I see to a ruler calling for a trial is well, King Joffery. But it does make sense in this situation so I'll allow it for a write-in.
Asoiaf may treat Trial by Combat differently
The wiki saying that nobles and knights can always demand Trial by Combat and may never be refused really raises my eyebrow, for instance
Historically, Trial by Combat existed to resolve matters when a guilty party couldn't be readily determined
It wasn't really intended to be a "get out of jail free card" for nobles to employ when brought to court by a higher authority
If your guilt was considered obvious then you generally couldn't weasel your way out of it by demanding Trial by Combat
You could request it, but the person presiding over the trial determined whether to grant it or not
I don't know if "Trial by Combat is a thing that nobles and knights always have access to as a last ditch effort to avoid punishment" is really a thing in Westeros either, in practice
I feel like I could go searching for cases where the accused ought to have tried to go for Trial by Combat if that option really was available to them and something they had control over rather than the guy presiding over the trial
Like if a lord attempts a failed coup and gets formally tried for treason, it'd be really strange if they could demand trial by combat for something they are very obviously guilty of, and then potentially win and get off scot free to presumably do it all over again later
No ruler is going to entertain the idea of letting someone who just tried to overthrow them walk away, surely
Granted, Arnold basically just tried to do exactly that recently
But I saw that more as him managing to dangerously sway public perception due to Rhaenyra's inexperience giving him too much control over the narrative in the courtroom
She could have denied him Trial by Combat, but it would have risked making him a martyr at that point
Because he managed to weave a narrative that he was a doomed hero acting in the interests of the Vale
So we ended up in a position where the move was to entertain Arnold's demand for trial by combat, so that we could personally crush him and take all the wind out of the sails of his rhetoric
Plus Rhaenyra was furious to the point that she wanted to grant the request just so she could put him down herself
At any rate
[X] [first] Suggest that Whitehill and Forrester each put forward a champion to determine whether the armsman belonged to house Whitehill or not in trial by combat. If he is determined to belong to Whitehill then they have a responsibility for the actions of their armsman, even assuming Lyanna did not order it of him, and so must pay for the reconstruction of the dam. If he is determined to be unrelated to house Whitehill then they owe Forrester nothing.
I think this works, unless anyone notices anything I missed