I have the same problem. Not working on Safari or Chrome. But it is working on my iOS devices.
Following thread
Lesson challenges suddenly stopped working

I'm having the same issue since 3 days. I send a mail to support who adviced me to use chrome or firefox. But i've tried both. Also tried differen't platforms and reinstalling browsers to no effect. Please fix!

First, thanks for the responses! Good to know it's not just me. Second, it would likely be helpful for the developers if everyone would mention approximately when they first noticed the issue.

Additional information: when using an incognito/private tab without logging in, lesson challenges work. After logging in (both in the incognito session as well as normal tabs) and attempting to access the same lesson challenge, the same aberrant behavior presents. Normally I'd suggest just using an incognito tab and not logging in as a workaround, but some lessons (including those I'm trying to use) require an upgraded membership (which I do have).

Additional information: when using an incognito/private tab without logging in, lesson challenges work. After logging in (both in the incognito session as well as normal tabs) and attempting to access the same lesson challenge, the same aberrant behavior presents. Normally I'd suggest just using an incognito tab and not logging in as a workaround, but some lessons (including those I'm trying to use) require an upgraded membership (which I do have).
Have you tried clearing your browser cache? However, you still are logged in under incognito mode so your membership is counted and you'll get access to everything you should.

Have you tried clearing your browser cache?
Yes, that was one of the first things I tried.

Same here! Challenges after lessons do not work neither on Chrome nor Firefox, but they do work on the mobile app! I'm reporting a bug!

I would if our problem is related to this?
https://www.chess.com/blog/erik/incredible-second-wave-of-interest-in-chess?alert=content

I would if our problem is related to this?
https://www.chess.com/blog/erik/incredible-second-wave-of-interest-in-chess?alert=content
I wouldn't be surprised at all. They might not have the ability to scale up with demand, but on the other hand, if that was the case I'd expect the challenges to work "sometimes unreliably", not "never". I also think it's odd that they seem to work until logging in, which I'd normally associate with an account-related problem.

For at least a couple of us, the only issue is with the web app. The mobile app is working fine. I would be surprised if this was an account-related issue.

from Chess.com Support, workaround worked for me:
I'm really sorry about the issue with lessons' challenges! Our developers are currently working on fixing that bug. The workaround is to change your pieces animation type to "Medium (default)" in Pieces and Board settings here: https://www.chess.com/settings/board
[Update: solved - try changing animation type to "Medium (default)" and if that alone doesn't work, try changing the board and piece theme to standard. Thanks to Tirao and OwnerOfHell for sharing communication from support personnel and their own additional research, respectively.)
I was working my way through the lessons when suddenly at a lesson on deflection, the challenges stopped appearing. The videos play just fine, but the main area of the challenges never renders. I've tried restarting my system, hard refreshing the page, clearing my cache, and using different browsers - I've used Brave, Chrome, Edge, and Firefox - same results everywhere. Is there a known issue with lesson challenges right now, or has this maybe been encountered before? I'd really like to continue training. Thanks!