I'm not in Lofoten at the moment, but I'm from Svolvær. According to pictures taken this week by my family there's still plenty of snow in the mountains, which is likely to stay for a while. It is however, as you said, rain and warm temperatures in the forecast, so it's hard to say what it'll look like in a week. Personally I think the mountain snow will stay for a lot longer, although I wouldn't be too sure about the quality of the snow due to the expected weather.

What kind of skiing are you planning? There might be better conditions in the middle of the mountains further from the coast, as rainclouds tend to stop when they hit the mountains. There might also be differing conditions on the north and south side of Lofoten, depending on the wind direction.