To set Lynx to stop asking to accept, reject or ignore cookies you will need to go to it's config file and update a few lines.
First you'll need elevated rights to the file before editing.
Look in your /etc folder for the file lynx.cfg
Edit the following lines:
#SET_COOKIES:TRUE
Uncomment it and set it to false.
SET_COOKIES:FALSE
Then find this line:
#ACCEPT_ALL_COOKIES:FALSE
Uncomment it.
ACCEPT_ALL_COOKIES:FALSE
Then find these two lines and ensure they look like this:
PERSISTENT_COOKIES:FALSE
#COOKIE_FILE:~/.lynx_cookies