I would need some good hi-res shots to tell for sure, but it does appear to be a wool or even a silk or linen. It's either Something with a relatively loose standard weave, or I'm seeing the pebbley grain of a felted wool blanket... Or perhaps the pic is just grainy. Like I said, hard to tell without hi-res. Definitely doesn't look like a canvas. You're correct that it has a softer drape than canvas. A well worn/washed canvas wouldn't even behave like that.
SC has a point about wool being used heavily throughout the SWU. Lucas does appear to have an unhealthy obssession with the stuff, so it is a good candidate. If this scandinavian blanket is made with the stripe on it, I would take it as a pretty good clue. I doubt LFL went thru the trouble of silkscreening the cape, so it's likely it was found with the stripe.