I am an Italian noahide.
Unless I am mistaken, in terms of sexual conduct the prohibitions established by the Noahide Law are the following (see Rambam’s Mishneh Torah-Melachim uMilchamot 9:5):
Homosexual intercourse between males
I have not found in any halachic source a statement according to which the Noahide Law prohibits the Gentiles from practicing prostitution (in the technical sense of a paid sexual intercourse), obviously if the prostitution conduct does not integrate one of the four prohibited activities indicated above.
Is it therefore correct to say that prostitution, per se, is lawful for the Gentiles on the halachic level?
With this question I do not intend to assume an apologetic position towards prostitution, but only to frame the case on the level of the Noahide Law.
Of course I consider the hypothesis in which prostitution is not prohibited by the law of the national state, in which case I believe that such conduct is also prohibited by the Noahide Law , which includes, in its seventh precept, the command to establish laws and courts of justice.