Sand is Deep Well definately...anyone can sue anyone including individuals, corpotrations and goverment as well. US Embassy being a part of US Department of State or the US government, anyone who has contentions against the US government can definately sue the US Embassy. However the legal battle will be fought in terms of the laws of VISA issuing country which is at this moment is immensely in favour of the VISA issuing country NOT the individual who is not a citizen of the VISA issuing country. Host country , its laws or its govt. cant force any embassy or diplomatic mission of a foreign nation in any circumstance to grant VISA to citizens of the host country. The legal battle will be over before it is ever fought.