Helen - root rot generally occurs when plants are in poor draining soil which means the water stays in the soil around the roots.   We don't usually recommend a fungicide without knowing specifically what the issue is so I would take a closer look at your soil and see if the drainage can be improved.  Copper fungicides are most successfully used on aerial blights and stem diseases but are less effective on the control root rot.  Rather, you could improve the soil drainage by adding compost or other organic matter into the soil where you removed the Lambs Ear.  In most cases, root rot does not move to surrounding plants unless roots are touching so maybe just keep an eye on the other plants around the area.  More info in the articles below about root rot.

https://hort.extension.wisc.edu/articles/root-rots-garden/

https://www.extension.purdue.edu/extmedia/BP/BP-206-W.pdf

I am wondering if the whole area has poor drainage?  If so, another option is to replace plants prone to root rot (like Lamb's Ear) with ones that prefer moist soil.  Below is a link to an article that contains a list of some of these perennials.  

https://extension.psu.edu/plant-guide-sun-to-part-sun-wet-to-moist-soil

Hope that helps!