Hello!

To plant a new tree near where the old elm stood, you'll want to remove as much of the old root system as possible to prevent competition for nutrients and water. A good guideline is to remove roots within a radius of at least twice the size of the new tree's root ball.

For the Japanese lilac tree, you'll want to ensure that the root flare is slightly higher than the surrounding soil to prevent water logging and root rot. This means that the root ball of the Japanese lilac should be planted slightly above the ground level.

The best way to remove the roots is a saws-all or a chainsaw. It is always best to call for utility line marking to be safe. A borer might be a more targeted option, but it may not be as effective in removing a large root system.   There are many YouTube videos that will show you how other people have done the same job.  Different tips and tricks depending on the circumstance.

I hope this helps.  Please let me know if you have any further questions.

Thanks for asking ASKExtension.