The fastest route is via Gothenburg, then north along the Vaner-lake to the 45 inlandsvegen through the middle of Sweden.
If you want to see all of the Lofoten, starting in the north and leaving the Islands via the ferry Moskenes-Bodo is the best route. Follow the 45 all the way up to Gallivare, then take the E10-45 to Kiruna. From Kiruna, go west over the E10 towards
Riksgrenzen. At the end of the road, when you reach the e6,
go right (north) towards Bjerkvik. From Bjerkvik you just have to follow the road over the Vesterålen towards Å i Lofoten, which is the southernmost village on the Lofoten.
On this route you'll have to take one short ferry from
Melbu on the Vesterålen to Fiskebol on the Lofoten. Due to the strong current in the gap between the Islands, this can be a bumpy trip...
We took this route in 2001, and it took us 6 days from the south of the Netherlands to a mc-rally in Gravdal on the Lofoten.
One of our group was a girl with less then a year driving experience on a cb-1 ...
If you don't want to take the longer route over the Vesterålen,
you could enter the Lofoten directly via the Ferry Skutvik - Svolvear, or take a part of the Vesterålen-route by taking the Bognes-Lødingen ferry.
On these alternatives you can leave the 45a bit sooner,
just west of Sorsele there's a small, unsurfaced road to
Arjeplog, where you then can take the 95? Silvervegen north west
over the Polar circle towards the E6 in Norway. This route I took in 1995, starting in Gotenburg, and entering the Lofoten via the Bognes ferry on day 5 of our trip.. The route towards Arjeplog and the Silvervegen are very nice, a lot of reindeer and a totally uninhabited countryside...
As told by others already, the RV17 is the recommenden route when going back south, less crowded then the E6, scenery is a bit better, it just takes a bit more time with all the ferries..
After the ferry Moskenes-Bodø spent one night at the big tidal-stream Saltstraumen, great to see, and a great place to catch some fish...
As an alternative you could take a part E-6 and a part RV17,
which I did last years. In 2001 we strated at the Saltstraumen and followed the RV17 to Mo I rana, last year I followed the E6 to Mo I Rana form where I followed the RV17 all the way south to Trondheim, with a stop at Torghatten, a big rock-formation with a walk-through hole in at .. (and a nice camping at the foot of the rock)
A few tips for the Lofoten:
-the unsurfaced route from Fiskebol to Laukvik. In Laukvik there's a camping place at the coast, and in the nearby harbour we saw a fishingotter and some eagles last year.
-the viking-museum at Borg.
-the camping just north of Ramberg, an ideal place to see the midnight sun from a white beach.
- the Fishing village Nussfjord.
btw if you got time for it, you could even reconcider the complete Whale-route, starting at Senya, ferry to the Vesteralen, ferry to the Lofoten...
btw 2 if you need more info just mail/msg/pm...