Pretty yard, Sandi!
The lilacs are going to travel to the area with the best nutrients for them, so it makes sense it would go for your flower bed. They can easily come up 6-7 feet away. Best you can do is mow where you can, and cut them out of the beds.
And I almost hate to tell you this, but our place had a burned out house on it. Just a cellar left. We assume the owners had planted two lilacs around the 1900, one in front of the house, one in back. They now cover an area approx 40 X 60.