Lefty. How do you know that the culprit is the Lilac tree? Is this discrimination? I have always believed that all greenery loved getting their toes into water. I have seen Fig trees & umbrella Trees send out roots 30metres to get their toes into a water supply they even send roots along water pipes to find a source.
I believe you may have unreasonably blamed the Lilac tree, what happened to the presumption of inocence! Lefty. get a plumber to excavate & repair the faulty pipes. They are the Culprit.
Alternatively, have the drainage plugged & fill the drainage with a powerfull Herbicide. dont be allarmed if the next door neighbours prize philodenrum dies. However this does not fix the problem as the drainage is either broken or faulty. Fix the Problem not the result!