So... is Juushin Liger finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: January 27, 1990
Manga finished: January 01, 1990
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
In a near-future setting, monstrous beings known as Dragonites suddenly emerge and wreak havoc, inadvertently releasing an ancient evil called Drago from his prison. Drago, alongside Empress Zara, aims to conquer the world with their biomechanical army. Earth's defenses are overwhelmed, and humanity faces imminent destruction.
Amidst the chaos, a seemingly ordinary teenager named Ken Taiga discovers a hidden destiny. He is the descendant of a legendary warrior who once sealed away Drago.
When faced with the Dragonites' attacks, Ken awakens to his true power. He possesses the mark of the Liger and can transform into a powerful, armored warrior called Jushin Liger. He then decides to combat Drago and his forces, becoming humanity's last hope against the impending darkness.