The US is a signatory to the Rome treaty, and this lawsuit would be in American courts not under purview of the ICC.
It is not a signatory to the International Criminal Court and was one of 7 that voted against it.
https://en.wikipedia.org/wiki/Rome_Statute_of_the_International_Criminal_Court
Finally the General Assembly convened a conference in Rome in June 1998, with the aim of finalizing the treaty to serve as the Court's statute. On 17 July 1998, the Rome Statute of the International Criminal Court was adopted by a vote of 120 to 7, with 21 countries abstaining. The seven countries that voted against the treaty were
China, Iraq, Israel, Libya, Qatar, the United States, and Yemen
This is sometimes confused with the International Criminal Court of Justice, which the US withdrew from after the court ruled that its covert war against Nicaragua was a violation of international law. The US used its veto to prevent the enforcement of the UN security council where the US was to pay compensation.
https://en.wikipedia.org/wiki/International_Court_of_Justice