Most of the time I drag the bush out, but I have used the FEL if the bush is located in an area where I have trouble getting to with the back of the tractor. If the bush is real stubborn I lower the FEL and will dig to China to get it out. ( an anger management problem I have)
I have a log chain that has a 3 inch round loop on one end and I thread the log chain around the bush, through the loop, hook the chain to my clevis on my draw bar, and slowly pull the bush out. As the chain tightens around the bush, it rarely slides off. I have never pulled Lilac so do not know the root pattern but I have done this to some very hardy bushes and it has worked well for me. I have a John Deere 2010 and it is around 45 horse power so they come out quite easily. Any thing I want to keep I dig by hand, trying my best to limit any plant damage, load it into my FEL and move it to where I want to transplant it.