Star Trek: Voyager premiered when Star Trek: Deep Space Nine was almost halfway through its third season. A darker version of Star Trek, Deep Space Nine had more convoluted storylines that did require regular watching unlike its predecessor Star Trek: The Next Generation. Voyager was much like The Next Generation in that it returned to episodic viewing, allowing fans to tune in as they would like and not miss too much character formation or big issues.
Voyager struggled a little bit in the ratings as did all the Star Trek series. There was never one that was a massive hit out the door during the Berman era. But Voyager held its own with tight storylines and characters that made viewers tune in weekly. Though not everyone was thrilled with certain characters, that didn't stop them from watching.
Over the years, fans have expressed discontent with Neelix , Kes , and even Chakotay , with Red Shirts Always Die's Chad Porto most recently writing that Kes "was a badly written and conceived character, played by an actress who didn't have the impact needed to bring new fans in." But Lien, like most of the cast of Voyager, wasn't the main character that drew in the fans. That honor belonged to Kate Mulgrew's Captain Janeway.
The arrival of Jeri Ryan did boost the show's ratings, but I don't believe for a second that Lien's departure was what saved the series. She could have remained on the show even with Ryan, and the series would have continued. Quite frankly, Lien's character was overshadowed by the other characters, and I don't think the writers knew what to do with her character. Had they given her more fire like they did when her character was possessed by an evil warlord, she would have been a much better asset to the series. In fact, they needed someone who was going against the grain, which is part of what Seven of Nine was.
There wasn't much conflict on Voyager initially even though writers had the opportunities to utilize the Marquis vs. Starfleet as major enemies. Bringing on someone that didn't want to be aboard Voyager added that extra element of tension the show needed. If the writers had tweaked Lien's character, maybe even allowed her to keep some of the personality she got when she was possessed, they would, most likely, have seen a rise in the ratings. Everyone getting along like best friends, for the most part, hurt the series more than Lien's character. More conflict was needed, and that was what Seven of Nine brought.