Bicicleur,
I don't know why do you think that it was a battle between a "southern" and a "northern" groups?
I rather see it as a battle between a "western" and an "eastern" group. Of course genetically, North-Western Europeans are "more southern" than North-Eastern Europeans, due to having more of Neolithic admixture.
So Nordic Bronze Age would be genetically more "southern" than Lusatian culture. Just like modern Germans are genetically more "southern" than modern Poles, as explained long ago by Davidski on hi blog:
http://polishgenes.blogspot.com/2014/01/poles-more-indigenous-to-europe-than.html
But geographically, of course Poles are more eastern, not more southern.
Genetic "southernness" vs. "northernness" is only about the amount of ENF vs. HG.
Here is a good map showing the amount of Northern Euro admixtures in K36:
This includes the following admixtures:
North_Atlantic
French
North_Sea
Central_Euro
East_Central_Euro
Fennoscandian
Eastern_Euro
Volga-Ural