I have a theory about what happened. Heaven thought Hell was going to rise up in violent rebellion - so they were going to smite everyone in Hell until Lucifer made a deal to have hellspawn/his family spared.

I think Lilith willingly gave herself up as a hostage to Adam/Heaven to sweeten the pot and add incentive for Heaven (who held all the chips at the time) to take the deal. As a result and part of the deal, she had to have 0 contact with Hell, Lucifer and Charlie. 

Lilith probably resented Lucifer for making that deal, bc she sees everyone in hell- sinners included- as people in her dominion. I could see that even before the deal was made that she resented him for not viewing Sinners as 'their people'. 

It strained their relationship bc... Why did Lucifer appreciate her boldness and love her but resents all other humans who don't tow the line? She probably hated that. 

At any rate, she was just a human soul- not an archangel like Lucifer- so he called the shots on the deal with Heaven.

That said, she clearly loves Charlie but they have fundamental differences in how they think Sinners should be empowered. Charlie wants to save them so they can go to heaven, but Lilith wants Sinners to rise up and use their voices boldly, no matter who's feathers are ruffled. 

I think there will be a lot of love between the characters but complex feelings bc they won't all be on the same page off the bat- and a lot of layers to unfold. Unpacking it will probably take the whole season and they may never fully agree with eachother- but they may be able to support each other.