Lilith puts her talents to good use (more evidently so than her chaotic husband). With her wealth and face and voice she has streetwise armies at her beck and call to resist the reaping forces of Heaven. It's a demanding cause to commit to though.
Messages used to come from her daughter at least once a day. Charlie's latest missed call is the first in weeks.
Lilith spares a short glance at the illuminated hellphone, before returning to the infirmary, where injured, fading demons lay stacked on stretchers. The Extermination was last night, and these are just some of the victims – those who rallied and fought back.
She's likely calling about her new project. It's futile to pursue redemption, Lilith thinks (knows), but the hotel has its merits; perhaps as a safe refuge for the least-damned (but damned nonetheless).
Charlie can be overly optimistic, but Lilith appreciates that her daughter also finds the genocide senseless, unjust, cruel. It's simply that Charlie never Fell (or was pushed) like her parents; that she's never experienced Heaven's unforgiving wrath as they did.
...
Perhaps she should return Charlie's call. It's been months since mother and daughter last spoke.
But there are many demons to tend to and pull from the brink here, now as for every year. Charlie has her own lover, and Razzle and Dazzle. These casualties have too few to help them all.
So Lilith tends and comforts those she inspired; and allows that regret to linger.
There's a moment in the opening scenes of the Hazbin Hotel pilot (around 1:06 in) where a 'Resist!' poster with Lilith's silhouette and name can be spotted. I chose to expand on that and headcanon that Lilith is heavily involved with those in Hell who make a stand against the Exorcists – holds concerts to raise funds, uses her standing and reputation to recruit & encourage demons through propaganda, and (as here) assist with the aftermath of Extermination days.
It also gives her a somewhat valid reason to not have time to return Charlie's calls, especially if Charlie is closer to Lilith than she is to Lucifer. I suspect Lilith could understand her daughter's reasons for pursuing redemption a bit better than Lucifer – I might aim to explore his POV in a later chapter.