If you are in LV, neither the mirror, not shutter are blocking the sensor, period.
When you take a picture, the mirror might come down and then up before the shot it taken, depending on the mode. It's been so long since I messed with my settings, but I know I always use silent mode 1 and the mirror does not move (so it is the same as mirror lock-up) and only the shutter moves (I think also only at the end of the exposure - I *think* the start is electronic in this mode).
As long as you do not shine a laser into the camera you are very unlikely to damage the sensor (however, this is a known issue when using video around lasers - don't do that). You possibly could with a long lens pointed directly at the sun (like maybe a 600+mm or something), although I've never heard of anyone doing/trying this.
I always use LV on a tripod for landscape, which not only include sunsets/sunrises, but also daytime with the sun in the frame. No problems, the light intensity is no where near enough to damage the sensor, even leaving LV on for 10 minutes at a time. Think about the fact the sensor is designed to shoot video outdoors for at least hours at a time and can't be restricted to never pointing it at the sun.