Ideas about what? Sure they can be transplanted. Make sure she doesn't have any apple trees around. Lilacs host anthracnose.

Ideas on how I should do it and what I need to do to prepare the trees for transplanting.

Please forgive me as I am new to the whole tree thing and trying to fix them. My lilacs are right beside my 3 apple trees and my cherry tree, is this causing the problem with my apples? My pear tree is also in the group but we seem to get edible fruit from this tree.
Barb

Barbydoll6- Transplanting Lilacs is the easiest plants to move. You can easly dig out some of the sucker shoots from the base of the shrub/tree with a sharpened shovel and make sure you leave a lot of root mass. Place the sucker plant in a plastic bag to keep moisture in during transporting. It is best to water the plant daily for a few days prior to your digging. If you want to move the whole plant, then you have to plan on digging around the dripline of the shrub/tree to a depth of 12-18 inches working in a slight angle toward the center of the plant so that you can break free the root system from the ground. If it is bigger then you even by a little, then you might want a skidsteer with forks to lift it out of the hole, or you have to work it out like the egyptians did with moving large stone.
Hope this helps out a little!

Can you tell me if it is safe to transplant a sucker lilac during the summer ?

Fall is usually better, however I move small seedling trees of all kinds all summer ling most survive with lots of watering. If they are going to die usually let you know right away.