I've followed steps on page Import from Last.fm:
1. In 1st step entered my Last.fm username,
2. In 2nd step dragged Import Last.fm to ListenBrainz
3. In 3rd went to Last.fm library
4. Clicked on bookmarklet.
5. Popup window appeared with "Sending page 0 of 589 to ListenBrainz" "Please don't navigate while this is running" "v1.3".
6. No other progress visible.

In browser's developer view I've clicked on Network tab and found out that respond to all submits is HTTP 500 Internal Server Error with additional text "Cannot record listen at this time".

There is no outage info on https://listenbrainz.org/current-status so I expected the service working.

Tested on: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/48.0.2564.109 Safari/537.36

Further details:
I've setup local server listenbrainz server. I'm not sure which code is listenbrainz.org running so I blindly tested some commits:

• master HEAD, which generates bookmarklet with version 1.4
• 33a8234 - last commit with bookmarklet version 1.3
• 13e158b - first commit with bookmarklet version 1.3
  All these worked - server responded "success" and all last.fm pages were parsed/imported.

Therefore my guess is listenbrainz.org is somehow broken or misconfigured.