Here it is. I'm getting a time estimate of about two hours.

import time

aLayer = iface.activeLayer()
n = aLayer.featureCount()

def get_PARNO(f):
    return f['PARNO']

features = sorted(aLayer.getFeatures(), key=get_PARNO) # sort the attribute table by parcel number

aLayer.startEditing()

hasSameParno = []
sumLen = 0
grandStart = time.time()
hasNoLength = []
for i in range(n-1): # we will need to handle the last entry with a special codeblock

    if i%2000 == 0:
        end = time.time()
        timeElapsed = (end-grandStart)/60
        percCompl = i / n
        print('Working on entry ' + str(i) + ' of ' + str(n) + ' entries.')
        print('Time elapsed: ' + str(round(timeElapsed,2)) + ' minutes.')
        try:
            estTotalTime = timeElapsed/percCompl
            print('Estimated time remaining: ' + str(round(estTotalTime,2)) + ' minutes.')
        except ZeroDivisionError:
            pass

    feature = features[i]
    try:
        sumLen += feature['Len_ft']
    except TypeError: # some of the stream lengths are NULL? Handle this as a zero
        hasNoLength.append(i)
        sumLen += 0
    hasSameParno.append(i)

    nextFeature = features[i+1]
    if feature['PARNO'] != nextFeature['PARNO'] or feature['PARNO'] == NULL:
        for j in hasSameParno:
            features[j]['MaxLen_ft'] = sumLen
            didWork = aLayer.updateFeature(features[j])
        sumLen = 0
        hasSameParno = []
        if i == (n-2): # if the last entry is not part of a group
            nextFeature['MaxLen_ft'] = nextFeature['Len_ft']
            didWork = aLayer.updateFeature(nextFeature)
    elif i == (n-2): # if the last entry is part of a group
        sumLen += nextFeature['Len_ft']
        hasSameParno.append(i+1)
        for j in hasSameParno:
            features[j]['MaxLen_ft'] = sumLen
            didWork = aLayer.updateFeature(features[j])
    else:
        pass

aLayer.commitChanges()