I had the same reaction about the Lilly of the valley until I did some research. The plant they showed on Outlander is: Maianthemum dilatatum ( Wild Lily of the Valley) instead of the one we are familiar with: Convallaria majalis ( Lily of the Valley).
This post talks about it and there are pictures of it that look very similar to the one showed on Outlander .
https://namethatplant.wordpress.com/2011/05/16/a-hosta-imposter-and-other-relatives/