I'm not as put off by the race-based/gender-based humor as some others are due to it being potentially funny in the right scenario (e.g. Eddie Murphy, Richard Pryor, Dave Chappelle, etc etc). What sets this show apart from its contemporaries isn't the race or sex of the host, it's the complete inability to relate any topic towards the audience in a fashion even remotely resembling comedy.
It would be easy to lay this at the feet of the host though it's just as likely a tandem effort including the crew behind the scenes. What is apparent is that the natural comedic abilities of the writers (assuming there is any) is incapable of overcoming the host's shortcomings as a host in the first place.
A late night show needs one of two things: A hilarious host or a competent writing team, preferably both.
You can see the former during a show's "remotes", a good example being Conan's Travels or his skits with his producer or Kevin Hart and Ice Cube. In these instances there is no writing, it is just a series of conversations and events that the people involved are able to present in a funny way. The best example of this, in my opinion, is Craig Ferguson's old show. Rarely was anything written, it was simply Craig's innate comedic ability and rapport with his guests and robot sidekick.
You can see the latter in a show like the Daily Show, specifically under Jon Stewart, arguably one of the most well-written shows of this sort in television history.
This one has neither. Lilly is the foil to Craig Ferguson. There is no chemistry with the audience, and it's obvious she has no stand-up experience (often considered a prerequisite for the role) to lean back on.
The writers' addition to the show is negligible, at best. Whereas the Daily Show presented Stewart with a gold mine, these writers seem as if they are using a template from Microsoft Word, circa Windows 97.
The format is dated and overdone, the skits are more fitting from an entry-level YouTube personality, and the bits about her "dancing on her haters" is difficult to watch simply because it is a perfect metaphor for the show itself: Genuine criticisms of the show are laughed over by (what I must assume to be) an audience on laughing gas while the host dances in a painfully awkward manner. Incapable of answering the critique, they choose instead to silently ignore the obvious concerns while still maintaining the out of "Hey, at least we read them on the air."
The format she comes from is geared towards young children. The issue being she has not transitioned from that format to a new one. This is mainly a problem because, despite what NBC had in mind, children don't watch late night talk shows. Especially shows in her time slot.
There is hope in the future, however, but not until the show either:
A) Changes the format.
B) Hire a better or larger writing staff with autonomy.
C) Lilly evolves on her own as a comedian to overcome A and B, though this option is unlikely as it's mostly predicated on natural ability.
All in all...it's a pass from me, for now at least.