There's no means of setting a domain level cookie and making it not visible on given sub-domain. (You will however need to prefix the domain with a period as such...)
ini_set('session.cookie_domain', '.domain.lk');
However, if the static domain doesn't require cookies (or indeed presumably the existence of PHP at all), the fact that this cookie doesn't exist shouldn't be an issue.
That said, you should be able to overcome this using the mod_headers Apache module on the given sub-domain (so that it's not transmitted to the browser client) via...
RequestHeader unset Set-Cookie