I wasn't able to find any comprehensive answer on this. Essentially, I am forwarding my godaddy domain pildora.info to sherm4nlc.pythonanywhere.com. The forwarded version of the site, won't display the favicon.
After enquiring godaddy, I got this answer:
[...] the favicon feature depends on how you built your site, I recommend to use forward only for this to work or figure out how favicon will work on masking, this question can only be answered by your hosting provider since the site is not with godaddy.
Is there any known way around this?