Would “lo” also be correct?

Hola Shirley

Yes, "su madre lo habrá reñido" is also correct. In fact, the verb "reñir" is a transitive verb so, technically we should be using lo/la for him/her, but this verb is very often used with le (for him and for her), and it is accepted. This verb could be in my opinion in the category of "verbos de afección psíquica" which is basically a group of verbs conveying some kind of change in the mood of the person. With these verbs, the use of "le" instead of "lo/la" is quite extended and accepted. 

I hope it clarified it.

Saludos

Inma