Hi,
If you start on stage 3 at the end of May you will certainly cross some snowy parts on some passes but you should normally not need any crampons or snow shoes to walk on the hard snow.
You can look on the Lofoten webcams a week before you are coming to look at the snow level (which differ from year to year
We (me and my dad) are going to do the long crossing from north to south, starting at the end of may from trekking day 3 (we skip the first two days) until the last trekking day 11. Do you think we need snow shoes / crampons?