Almost certainly not. The consensus is that most of the early raiders came from Norway. It seems that they took up raiding to compete with their southern neighbors. Charlemagne's empire was expanding at the same time that trade routes were growing out of Frisia (modern Netherlands) into such towns as Ribe (DK) and Åhus (SE). These towns gave elites in south Scandinavia access to rare foreign goods, and it seemed like Norway was being left behind. So the Norwegians started taking foreign goods through violence, in competition with their south Scandinavian neighbors.

From this perspective, it's doubtful that the raid on Lindisfarne had anything to do with Charlemagne's invasion of Saxony. It is, however, very interesting that they both happened at about the same time, and that the small raid on Lindisfarne is remembered as such an awful event while Charlemagne's invasion of Saxony is seen as part of the almost "natural" process of state-building.

Regarding medieval religion, it's important to recognize just how diverse things were. Latin sources did sometimes group people as "Christians" or "pagans" but it's hard to imagine these groups working together as coherent communities. North European Christianity was focused on monasteries connected through the personal relationships of churchmen, surrounded by a sea of popular religion that could've been just about anything. North European paganism, on the other hand, had nothing at all holding it together, so it was probably highly localized.

Some god names might have been popularly used, and there were certainly a few popular stories told in similar forms everywhere, but there's no real evidence of a common set of beliefs or practices. In some places, there seems to have been a head cult, whereas in others, sacrificial victims were strangled or stabbed. The pagans of Lindisfarne and Saxony may have had as little in common as today's Christians of Mormon Utah and Orthodox Moscow.