So... is Luck & Logic finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 26, 2016
Manga finished: April 08, 2017
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 the world of Luck & Logic, beings from other dimensions known as Foreigners threaten humanity by using "Logic," the essence of everything abstract.
To combat this, an organization called ALCA employs Logicalists, humans who can bond with friendly Foreigners and utilize Logic to fight back.
The story focuses on Yoshichika Tsurugi, a former Logicalist who lost his powers. When he meets Athena, a goddess from another world, he regains his abilities and joins ALCA.
Yoshichika must now work alongside other Logicalists to defend their world from the invading Foreigners.