Can see anything and everything
Lilith actually forgot to tell Lucy that Lith just arrived in the Vampire Continent. However, it mattered little, as Lucy felt Lith's emotions within the next few seconds and thus she kept quiet.
Lilith was able to see both Lith and Lucy. In fact, she has the ability to see anything and everything in the world if she so desires. She possessed the power to do so. However, she couldn't care less about anything or anyone else, so she limited her range to just her two children.
Watching them grow and their day to day lives and activities seemed very fun to Lilith. She could feel as if she was taking part in their activities just by watching them. She would also sometimes feel the need to intervene but would always stop herself from doing so as it would result in a halt in her children's growth.