On the ERJ-145, I was told one could lose both in the event of a bad strike.
For this reason we were advised to start the APU if a strike looked likely.
The -145 had FADEC equipped engines.
I was told the same thing by a UK operator, however; it's more a CAA dictated procedure, because they are concerned about both tail engines being too close together. This came from a TRE.
I have not heard about a similar procedure from either Embraer or US operators. I had two lightning strikes in the E145, one on the approach to PHL, the other into MAN and never had any resulting engine/FADEC issue. Some damage though...
FADEC systems have their own dedicated generator on each engine.
Additionally, they are usually located to the center of the fuselage to prevent any interference from lightning strikes etc. The famous Michael Faraday had shown that electricity doesn't penetrate the center of a cage/frame/car, etc.