In your case of a non-Jew giving someone equipment for a job, that equipment was always the property of the non-Jew. It was never lost. Keeping it against the owner's will is theft.
The fact that the owner is a non-Jew doesn't make it any less of a theft. It is true that the gemara in Sanhedrin and the Rishonim discuss whether one should return an item lost by an idolater but (1) modern non-Jews might not be the same idolaters, (2) it is forbidden to keep such an object if it would create a chilul Hashem and (3) it is explicitly permitted to return it if it creates a kidush Hashem. See here on MY for more details.
In any case, your case is not one of a lost object. And regarding robbery from non-Jews the Rambam writes (MT Gezelah v'Avedah 1:2)
It is forbidden to rob even the slightest amount. It is forbidden even to rob or to withhold money from a gentile who
worships idols. If one robs or withholds money from such a person, one
must return it.