Is ghusl obligatory if a man looks with desire, and then, two hours or more after istinja, thick white fluid, similar to semen, is discharged, even though its discharge was not with desire?

Most likely, the fluid discharged after urination is wady and not maniy (semen). Wady is a thick, white fluid that usually exits after urination. Its ruling is the same as urine, in that it is impure and necessitates istinja' (washing the private parts) but not ghusl (ritual bath). If the questioner doubts whether the discharge is maniy, ghusl is not obligatory for him, because the default is non-obligation, and doubt does not remove this default. One must lower his gaze from what Allah has forbidden.