It's by design. According to the Homebrew homepage:
Homebrew won’t install files outside its prefix and you can place a Homebrew installation wherever you like.
According to the lynx man page:
LYNX_CFG This variable, if set, will override the default
location and name of the global configuration file (normally,
lynx.cfg) that was defined by the LYNX_CFG_FILE constant in the userdefs.h file, during installation.
In some linux distribution, the constant
LYNX_CFG_FILE in set to
~/.lynxrc (as I remember) but in Homebrew this constant is left to its default value. You can check it with
brew edit lynx. If you want to change the location of the lynx configuration file, you have, as you tell, to set: