why does the Judge Domínguez pretend to be Letal?

what's that for? he is a cop he got job to do.He said he invented a character to infiltrate a case he charged of.But it seems he had been pretended to be letal a month before Rebecca's husband being killed(he and Rebecca screwed).Does he can predict Rebecca will kill her husband beforehand? Or you can say he just played it for fun or to approach Rebecca