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Yes, go ahead and plant it out into a shady part of your garden. Give it plenty of water over the first few weeks as we are entering the warmer temperatures of summer.

https://www.gardeningknowhow.com/ornamental/bulbs/lily-of-the-valley/growing-lily-of-the-valley.htm

What type of trees are you working with?
Removal of roots can be detrimental to a trees health.

I would suggest consulting with a Arborist to determine if the removal of small roots will harm your trees.

http://www.arborilogical.com/newsletter-archive/2011-spring/removing-exposed-tree-surface-roots/

Late Fall is the best time to plant.
Here is a link with more information.
https://www.gardeningknowhow.com/ornamental/bulbs/lily-of-the-valley/growing-lily-of-the-valley.htm

Are there brown or yellow spots on the leaves? Has there been a change in watering?

Yes. The seeds should be planted either indoors or outdoors immediately after harvest. See this article:
https://www.gardeningknowhow.com/ornamental/bulbs/lily-of-the-valley/lily-of-the-valley-seed-pods.htm

You didn't say where you live, but Lily of the Valley is pretty hardy. It will tolerate the cold, but you may want to introduce it to outside conditions slowly (over a few days) by putting it out in a partly shady part of the yard during the day and bringing it in at night. https://www.gardeningknowhow.com/ornamental/bulbs/lily-of-the-valley/growing-lily-of-the-valley.htm