I bought a starter lilac tree which came with its roots wrapped up. The leaves started to dry up, so I replanted it into a pot. The leaves continued to fall off. I water it every other day and all of the leaves fell off. I don't want it to die all the way. What should I do?

Stop watering With few if any leaves it did not need water. As lilacs are essentially weeds (don't get me wrong - I have a huge collection of different ones ) I would recommend re potting in new/just moist soil and leave it in a cool lit area.