Q.Why Are Lilac Flowers Growing Underground?
I have a mature 10 foot lilac and the flowers on the actual shrub are gone but I have lilac flowers popping up on the ground around it. I dug around the one and it was in flower around 4″ inches below the soil level and appears to be growing from a root. I noticed the biggest one nearly two weeks ago and it’s still in flower. Has anyone ever seen this and what caused this?

Certified GKH Gardening Expert
Because of the way the crown is situated in lilacs (underground), and the flowering habit (on new wood) this can be a common occurrence. The soil has kept the area around the new shoots at a suitable temperature and moisture to produce flowers.
You can choose to leave the "suckers" or you can remove them. Either way will not harm the shrub. Removing them creates a more compact, tidy shrub. Leaving them creates a broader, more "shrubby" shrub.
Here are some articles that will give you more information about the plant: