I'm a long-standing fan of the writings of James H. Schmitz, the author of a number of remarkable science fiction novels and stories originally published between 1960 and 1974. I enjoy them for their bold female characters (surprising even by today's standards), for the author's deft handling of psionics, and for his surprisingly accurate forsight of certain technologies such as cell phones and biotech. The TV series Babylon 5, and the recent Vorkosigan novels by Lois McMaster Bujold, owe something to the excellent legacy of Schmitz and especially the Telzey character of this and other Schmitz books.
Many of Schmitz' writings fall into one of two universes and have many interlocking characters. He wrote one set of tales set in the universe of the "Agent of Vega" series. He created a different universe in the "Federation of the Hub" series which includes over two dozen stories and novels (this is the second novel set in that environment). His writings exist as eight novels and fifty-odd stories in several collections, most of which have thankfully been reprinted by Baen books.
This is a fun read, and it's even more fun if you've also previously read THE UNIVERSE AGAINST HER - Telzey Amberdon Book (1) One (by the author of The Witches of Karres).
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.
This novel was first published as a two-part story in ANALOG in August and September of 1971. 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.