(UPDATE: Seems to work now. Can't delete the bug report, unfortunately.)

Launcher gets a 403 error when trying to download https://libraries.minecraft.net/tv/twitch/twitch-platform/5.16/twitch-platform-5.16-natives-linux.jar and won't launch, even after giving up (last part of error message shown - repeats several times before this).

...
[12:59:30 INFO]: Attempting to download /home/krista/.minecraft/libraries/tv/twitch/twitch-platform/5.16/twitch-platform-5.16-natives-linux.jar for job 'Version & Libraries'... (try 5)
[12:59:30 WARN]: Couldn't download https://libraries.minecraft.net/tv/twitch/twitch-platform/5.16/twitch-platform-5.16-natives-linux.jar for job 'Version & Libraries'
java.lang.RuntimeException: Server responded with 403
at com.mojang.launcher.updater.download.ChecksummedDownloadable.download(ChecksummedDownloadable.java:97) ~[launcher.jar:?]
at com.mojang.launcher.updater.download.DownloadJob.popAndDownload(DownloadJob.java:108) [launcher.jar:?]
at com.mojang.launcher.updater.download.DownloadJob.access$000(DownloadJob.java:12) [launcher.jar:?]
at com.mojang.launcher.updater.download.DownloadJob$1.run(DownloadJob.java:89) [launcher.jar:?]
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:471) [?:1.7.0_51]
at java.util.concurrent.FutureTask.run(FutureTask.java:262) [?:1.7.0_51]
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145) [?:1.7.0_51]
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615) [?:1.7.0_51]
at java.lang.Thread.run(Thread.java:744) [?:1.7.0_51]
[12:59:30 ERROR]: Gave up trying to download https://libraries.minecraft.net/tv/twitch/twitch-platform/5.16/twitch-platform-5.16-natives-linux.jar for job 'Version & Libraries'
[12:59:35 INFO]: Finished downloading /home/krista/.minecraft/versions/1.7.9/1.7.9.jar for job 'Version & Libraries': Downloaded successfully and etag matched
[12:59:35 ERROR]: Job 'Version & Libraries' finished with 1 failure(s)! (took 0:00:10.140)