There is water everywhere and the Lofoten Islands are not yet concerned with pollution.
The only problem can come from the livestock (mainly sheep) that walk freely on the islands in summer.
Even if we often fill our water bottles directly in a stream or a lake and consume the water directly, it is more reasonable to purify the water that is not intended to be boiled. Either by using a filter or with disinfectant tablets. If you purify your water, you can take water anywhere along the route without having to check if there are animals around (which is often difficult).
To avoid any problems, you should either boil your drinking water, or use a filter or tablets.
There are small filters that are easily transportable (such as "Katadyn-combi"). The advantage of the filter, compared to tablets, is that it provides a water without any aftertaste (peat taste, chlorine), unlike the purifying tablets such as Micropur or the Aquatabs .