How strange! Schatzie my black kitty does the same thing. She is so terrified about being picket up that she only comes to me when I’m either lying down or sitting on the toilet.
Any other time when I reach down to pet her she shrieks and bolts.
When I’m lying on the floor very still, she comes to me sniffing my face and hair, sometimes even biting my hair.
Cats have such different personalities. Auggie is the complete opposite, fallowing me everywhere and demanding constant attention. She is my little stalker!
Hopefully with time Lizzie will become less aloof.
Rest assured that she loves you in her own way.