It's not in the sense of fitting it's if you'd find it interesting to see Chrono characters in the eras. Lavos was thought of though as a god by a number of the people in Chrono Trigger, so simply, he's recognized as god in any of these time periods. Or better yet, you could switch it up and have him be seen as a demi god, a Hades follower(believes he/she) is using Lavos as a minion of the underworld to cause chaos and allow the ruler of the underworld to rise and conquer. But alas, Lavos simply devours the life of it's "master". That's what i've got for my vote. I have other ideas too.
As for the other time periods, I dunno, just thought I'd put them there to give a few ideas of time periods everyone recognizes.