Using the approach suggested by Doron Yakovlev-Golani, I did it with this class:
public class LessonsLayoutManager extends StaggeredGridLayoutManager {
    private Point mMeasuredDimension = new Point();
    public LessonsLayoutManager() {
        super(2, HORIZONTAL);
    }
    @Override
    public void onMeasure(RecyclerView.Recycler recycler, RecyclerView.State state,
                          int widthSpec, int heightSpec) {
        final int widthSize = View.MeasureSpec.getSize(widthSpec) - (getPaddingRight() + getPaddingLeft());
        int width = 0;
        int height = 0;
        int row = 0;
        for (int i = 0; i < getItemCount(); i++) {
            if (!measureScrapChild(recycler, i,
                View.MeasureSpec.makeMeasureSpec(i, View.MeasureSpec.UNSPECIFIED),
                View.MeasureSpec.makeMeasureSpec(i, View.MeasureSpec.UNSPECIFIED),
                mMeasuredDimension)) continue;
            if (width + mMeasuredDimension.x > widthSize || mMeasuredDimension.x > widthSize) {
                row++;
                width = mMeasuredDimension.x;
            } else {
                width += mMeasuredDimension.x;
            }
            height += mMeasuredDimension.y;
        }
        setSpanCount(row);
        setMeasuredDimension(View.MeasureSpec.getSize(widthSpec), height);
    }
    @Override
    public boolean canScrollHorizontally() {
        return false;
    }
    @Override
    public boolean canScrollVertically() {
        return false;
    }
    private boolean measureScrapChild(RecyclerView.Recycler recycler, int position, int widthSpec, int heightSpec, Point measuredDimension) {
        View view = null;
        try {
            view = recycler.getViewForPosition(position);
        } catch (Exception ex) {
            // try - catch is needed since support library version 24
        }
        if (view != null) {
            RecyclerView.LayoutParams p = (RecyclerView.LayoutParams) view.getLayoutParams();
            int childWidthSpec = ViewGroup.getChildMeasureSpec(widthSpec,
                getPaddingLeft() + getPaddingRight(), p.width);
            int childHeightSpec = ViewGroup.getChildMeasureSpec(heightSpec,
                getPaddingTop() + getPaddingBottom(), p.height);
            view.measure(childWidthSpec, childHeightSpec);
            measuredDimension.set(
                view.getMeasuredWidth() + p.leftMargin + p.rightMargin,
                view.getMeasuredHeight() + p.bottomMargin + p.topMargin
            );
            recycler.recycleView(view);
            return true;
        }
        return false;
    }
}
The result looks like this:
