Not a fifth lens, but the point the whole engine exists to make: historians describe the same country differently because they weigh its causes differently.
The founding population is the sharpest dispute. The consensus and cultural readings describe a settlement of free Norwegian farmers who built a law-bound stateless order from scratch. The revisionist reading, resting on genetic and archaeological evidence, describes a more mixed and more coercive founding population — a majority-Gaelic female line, much of it unfree — and treats the “free Norse settler” story as a flattering simplification. The facts of ancestry are not contested; what divides the readings is whether that ancestry belongs at the centre of the founding story or at its margin.
Independence itself divides the lenses a second way. The cultural and consensus readings treat the republic of 1944 as the overdue restoration of a nationhood that language and law had preserved unbroken since the Middle Ages. The economic-geographic reading treats the same independence as substantially enabled by material opportunity — wartime disruption of Danish authority, American base revenue, and a booming postwar fish export trade — rather than as the pure fulfilment of a long-held cultural will.
On one point all four perspectives agree: Iceland’s central historical achievement is maintaining a cohesive, self-governing society against far larger outside forces — Norway, Denmark, Britain in the Cod Wars, the global financial system in 2008. They part only on what did the work of holding it together: law and consensus, elite power and dependency, language and faith, or the disciplined management of a narrow resource base.
Reference status: every work cited is verified and correctly attributed — Byock (2001); Karlsson (2000); Helgason et al. (2001); Ebenesersdóttir et al. (2018); Jón Viðar Sigurðsson (1999); Hálfdanarson (2012); Ásgeir Jónsson (2009); Jóhannesson (2004); Hannes Jónsson (1982). The genetic-ancestry proportions and the Cod War timeline are drawn from peer-reviewed sources; Jón Viðar Sigurðsson’s account of chieftain power concentration is a recognised scholarly reading of the Commonwealth’s collapse, not a universally settled one.