The Lion Game's two long episodes about Telsey Amberdon seem to follow directly after the The Universe Against Her. The lion story is partly mystery, with horror and science fiction thrown in. I found this book very scary the first time I read it. The first episode is easy to digest. Some people find the second one somewhat complex and hard to follow.
In the first story of The Lion Game, Telsey sneaks off from her friends during a camping trip to investigate a distress cry which she sensed. The story is all about what happens to her as a result. The second story is about the (somewhat later) aftermath to the first episode. Telsey finds herself hunted by the master minds she foiled in the earlier story, and she ends up travelling to another planet to confront them at the source.
This novel was first published as a two-part story in ANALOG in August and September of 1971. The cover shown is from the ACE second printing, 1985 edition, with cover art by Steve Durke.