First I’d suggest running the following:
%pip install ipywidgets skillsnetwork
Restart the kernel. Then try the import again.
If that doesn’t help maybe try the install command from the skillksnetwork documentation here substituting the following in the appropriate place:
piplite.install(['ipywidgets<7'])
Restart the kernel and try import ipywidgets. Then if that works try the skillsnetwork install command as it is written in the documentation.
If that fails you may need to contact who is running your JupyterLite site to see if they know the combination needed.
What you are reporting looks reminiscent of this issue here; however, it seems yours involves much older versions of the software? And it looks like this too.