I'll just say I agree with everything Lucky says.
I'll just add...patience! Three months is barely enough time for a somewhat insecure dog to adjust to his new environment; keep doing what Lucky says, be consistent but be aware it may take some time.
I've taken in two very fearful dogs - each took a minimum of one year before they REALLY started to blossom & become brave.
And you're totally correct about not using aggression or force. Imagine you are just terrified of something, and someone gets really angry at you for being afraid...you would not be likely to trust that person much. Lizzy needs to learn to trust that YOU will keep her safe...this is why obedience training is important because she'll come to rely on you for cues about how to act & react.
Good luck and stay with it! It is very rewarding watching a traumatized dog slowly gain confidence and knowing it's because of YOU.