daughter of Zion - the city (Psa 9:14), Jerusalem and its inhabitants (2Ki 19:21): “daughter” (feminine, singular being used as a neuter collective noun), equivalent to sons (Isa 12:6, Margin) [Maurer]. Metropolis or “mother-city” is the corresponding term. The idea of youthful beauty is included in “daughter.”
left - as a remnant escaping the general destruction.
cottage - a hut, made to give temporary shelter to the caretaker of the vineyard.
lodge - not permanent.
besieged - rather, as “left,” and Isa 1:9 require, preserved, namely, from the desolation all round [Maurer].