I'll try to suggest a few that aren't that well known. It will be a downgrade either way, but you can try these:
renpy - BOAT (finished); Monster girl 1000 (finished); My tuition academia (finished); harem hotel; corrupted kingdoms; mythic manor; goddesses' whim; Long live the princess (finished).
rpgm - The last sovereign (free on steam); Noblesse oblige (free on steam); Renryuu's ascension; Demons roots (finished).
unity (?) - Hush hush (finished); how to build a magnificent kingdom (finished); Unveiling the unknown (finished).
*all that are finished have either compelling stories or at least some sort of twist. From these, the best is magnificent kingdom but it's also the one with the most troublesome gameplay to get to that story. The easiest is BOAT. The most unexpected would be tuition academia's true end.
**from the unfinished ones, the best in terms of story is last sovereign, the other rpgm also try to tell a story but tls is almost done. The renpy ones are not that great in story, but lacking willpower to power through better stories with worse gameplay, they'll do.
Edit: As always, Higurashi; Tsukihime; Steins;Gate (original and 0); and the Fate series (especially stay/night and hollow/ataraxia) stand as overall recommendations due to their legacy to the genre.
The most relevant recommendation would be for you to watch the entirety of the Monogatari Series though, since it's on par if not superior to LiL in every way and deals with a lot of the same themes.