My plan is to replace the dry one soon (so the new one is established by this winter), cut off all the dead twigs down to about 3 inches from the root stock where there's a little green under the bark, replant it in it's own container out in back of the house and see what happens.
Could it be in shock or dormant?
I can't tell if it's in shock or gone dormant. Trees and shrubs will shed their leaves when stressed, as those are expendable. I'm a bit confused about what you say you are going to do though (happens to me sometimes)
I think what you are saying is that you want to cut back the lilac that appears to be dying, pot it up and put it in the back of the house to spend the winter in the pot. I'm thinking you are in hardiness zone 6, so you will have to sink the pot into the ground for the winter. I would suggest that you add some compost with a sprinkling of lime to the soil you pot it up with and mix it in.
Newly planted shrubs need water for about a year after planting. Take a look at these sites about how to plant, water and mulch (the same as for trees) newly planted shrubs.
Here's info on growing lilacs.