Animals often avoid eye contact, it's considered rude. Humans are a very touchy-talky-looky species. So yeah, it's freaky. I used to think I suffer from face-blindness (forgot the fancy name of it), then it occurred to me that I just straight up forget/avoid to look into people's eyes so I never even see their faces. Now I sometimes try to make a conscious effort to look at people's eyes - but how long is even appropriate?

Your story of the lemur reminds of staring into the eyes of a genet for probably about a century during a somewhat substance-enhanced camping trip. Can't say I was freaked out, rather honoured by the animal deciding to hang out with me for a while?