Since Line does not provide a web client or a proper desktop client for Linux, using Line on Linux is quite a pain. Currently, the single best option is to use the Chrome Addon, but even this method is not properly usable out of the box. After a bit of trial and error I have found the following workable setup:
Start Chromium by executing

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chromium --user-data-dir=~/tmp/chromium-line/

and install the Line Addon. Then obtain the link of the Line Addon page by opening Line in Chromium and viewing the page source by C-u. Let’s suppose you got the following link (like I did)

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chrome-extension://ophjlpahpchlmihnnnihgmmeilfjmjjc/index.html

You can then start chromium by executing (change ~/tmp/chromium-line to a value you like)

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chromium --user-data-dir=~/.cache/chromium-line/ "chrome-extension://ophjlpahpchlmihnnnihgmmeilfjmjjc/index.html"

and stop it by

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pkill -f "user-data-dir=~/tmp/chromium-line/" -SIGKILL

Starting Chromium with a custom user-data-dir has the advantage that your other Chromium instances are not contaminated by Line. Further we start Chromium with the extension link so that we don’t have to reopen the Addon page of Line.
Killing the Chromium instance instead of gracefully quitting has the advantage that we are not logged out of Line (as long as we have a internet connection the next time we start Line).