There are several places you can get water from the stream on the way up to LBSL. There is water at Clyde Meadow. There is usually some water flowing down the "cliff" up to Iceberg Lake.
I don't see why you couldn't filter any of these sources.
I’ve filtered water from Upper Boyscout Lake. It’s never been a problem. Of course, I’m not sure how some of the more popular lakes along the Mountaineer’s Route (like Iceberg Lake) compare in terms of contamination.