Are Noahides required to guard their eyes (Shemirat Eynayim) as Jews are? Is there some information in Jewish religious literature addressing this question?
The concept of guarding the eyes is set up to prevent one from forbidden relationships. The list for a Jew is enumerated here. The Talmud Yerushalmi Brachot 1:5 states that the eyes [and heart] cause one to sin (in the right context). In Nedarim 20a it also states that one who looks at forbidden relationship will eventually come to commit a sin.
Recounted by Rambam in Repentance 4:4:
He who wantonly stares at the opposite sex, for he thinks that it is of no matter, saying: "Have I stilled an urge, or even been near her"? whereas he remains oblivious to the fact that purposeful eye-staring is a great iniquity and begets actual unchastity, even as it is said: "And that ye seek not after your own heart and your own eyes" (Num. 15.39).
Non-Jews however, do not have a lengthy list of prohibited relationships; just six.
There are six illicit sexual relations forbidden to a gentile: a) his mother; b) his father's wife; c) a married woman; d) his maternal sister; e) a male; f) an animal.
It comes out that a form of guarding the eyes may need to be implemented, should such issues arise. But surely any method could work.
One of the primary prohibitions in looking at illicit material is that it causes improper thoughts.
מכאן א"ר פינחס בן יאיר: אל יהרהר אדם ביום ויבא לידי טומאה בלילה - כתובות מ״ו
The prohibition (see Igros Moshe E"H 1 §69) of improper thoughts is because it can cause הוצאת זרע לבטלה [wasting seed].
Whether or not Noahides have the prohibition of wasting seed would depend on the reasoning for the prohibition: If wasting seed is prohibited because of P'ru Urevu (Tosfos Sanhedrin 59b), a Noahide would not be forbidden (because a Noahide is not commanded to procreate [Tos. ad loc]. See, however, Tosfos Chagiga 2b, who implies that a Noahide is commanded in Pru Urevu, in accordance with the Sheiltos 165 and the pashtus of Yevamos 62).
If, however, the prohibition is from Lo Sinaf (או״ז א-קכ״ד, סמ״ק רצ״ב), a Noahide would indeed be prohibited from wasting seed.