Do you know what your USDA temperature zone is?

It can be a real challenge to keep containerized plants healthy unless you are sure of the proper water routine, fertilizer needs, light requirements, and more. The type of container mix makes a huge difference, too. It 'sounds' like you are unsure of these factors in regards to the care this plant has been giving.

Also, although Syringa x persica can survive in some difficult locations, it may not do so in a container. In-ground plantings help keep the root systems cooler than an above ground pot. Also, the root system of a planted shrub can grow like gangbusters in all directions, better able to survive heat, drought, freezes, over watering, and more. In a container, the root system is held totally captive.

You mean 'cambium', right? Just wanting to make sure.

I believe I am in zone 8b, possibly 9a. I have been told not to use fertilizer for the most part,as it can reduce or eliminate blooms entirely for the sake of leaves, and if I do to make sure it is low on nitrogen... something like an 8-20-16. The closest I could get was the rose fertilizer I had on hand, which is a 18-24-16, but I was willing to sacrifice blooms to gain some bulk on the bush and get it established. As for water, I tried to water it deeply a few times a week, making sure the soil wasn't water logged (until I realized my drainage had stopped up) but not dry either. We don't get a lot of rain here, so I tried to ignore everything I found saying not to water often. The lilac is planted in full sun, but because of how drastic it is here, it gets full a.m. sun, but some shade in the afternoon.
I unfortunately had to plant the lilac in a container since we are renting the house, and I really would like to take it with us when we move. Do you have any suggestions as to what potting mix I should be using? I used Black Gold general purpose potting soil when I planted it. I recently received a very small Miss Kim lilac, and want to make sure I don't make the same mistake with this one. Thanks!