Answer: To do their best, lily-of-the-valley plants prefer a good rich moist soil in a shady spot. In a spot that is too dry or too sunny the plants will turn brown and shrivel. On poor soil they will simply fail to spread into a lush carpet.
Unfortunately, it can be difficult to establish plantings under trees. Although shady, the soil directly under some trees can be very dry, partly due to the fact that the canopy prevents rain from reaching the ground, and partly because the tree roots absorb a huge amount of water from the soil. Any plant under a tree must also be able to survive with limited sunlight and nutrients as well as limited water.
The soil beneath the pine in all probability is quite dry and fairly acidic from years of fallen needles and the shade is dense. The soil beneath the maple in all probability will be full of surface roots and very dry; the shade is also quite dense. The soil beneath the oak will be a more favorable planting location, but probably still rather dry.
You might wish to experiment with several additional types of ground cover such as pachysandra, epimedium, English ivy and periwinkle (vinca minor) rather than trying just the lily-of-the-valley. I suspect you will find that different types do better under the different trees, and even perhaps from one side of a tree to the other depending on where/how the root systems have developed. Good luck with your project!
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