Up to Lofoten in March... -- Unlikely to find any snow on normal roads, depending a bit on whether early or late March.
There is always the possibility for a blizzard up to April, but they seem to be more and more rare. Adjusting to conditions is the key.
But yes, you still need legal tyres with 3 peaks marking. 3 peaks are further classified as Nordic type or Continental, where the Continental is better on wet roads above freezing and can take higher temperatures, while the Nordic type is better on ice and snow. The Vredestein mentioned above is a Continental type I believe.
If this is the only time you would need tyres for possibly icy roads, I would go with something you can use for other purposes as well, like the BFG AT. When new, they are quite good in the snow - not so good on ice. If the forecast says "icy roads", you can chose to postpone todays travel, or bring chains. You would have to check the handbook for use of chains though. (The 100 e.g. can only have chains on the rear. At the front they get too close to ball joints and height sensor)
If further north than Bodø - expect full winter.