This one should be (in theory) quite easy to work out. We know from the final panel that the Aniara traveled for 5,981,407 years before reaching its destination. We also know that its destination was the Constellation Lyra. Unfortunately, this is where the calculations break down a bit since Lyra isn't a place, but rather a cluster of stars that happen to be in the same direction when viewed from Earth, but sitting at dramatically different distances.
Assuming the ship hit a planet at Vega (the brightest and closest star in that constellation, 25 light years from Earth) the ship would have traveled at approximately (approx) 0.000004c (25.05 / 5,981,407), or approximately 1.25km/s.
Assuming the ship hit a planet at Gamma Lyrae (the farthest visible star in the classic Lyran constellation, 620 light years from Earth), the ship would have needed to be traveling at (approx) 0.0001c (619.7 / 5,981,407) or about 31km/s.
This, of course, doesn't remove the possibility that they traveled through Lyra and out the other side and hit something that was merely in the same direction.