Å ha lyst seems to be exactly like the German Lust haben, French avoir envie, Spanish tener ganas, Italian aver voglia, or English to feel like (or alternatives like to fancy or to have a hankering). "Want" very often conveys decision or demand; "feel like" only conveys desire.
Every time I come across something like "å ha lyst" I always think to myself "man, this is pretty weird" but then I go "wait... that's exactly how it is in French..." Since I'm learning from an English perspective I tend to compare everything to it and forget about my own native language. I tell you though learning Norwegian as both an English and French speaker makes it a whole lot easier. Pretty much every time something is very different from English, it's usually exactly like French. That's not even counting all the words that come from French too. All in all, I feel like I'm in a very good position to learn Norwegian and it feels pudding great.