^ To indulge in sweet, sweet ultracrepidarianism:
Per Wikipedia, human capture rate is only 20 - 25%, whilst gills can reach up to 90% efficiency. So the volume is prolly the same. Of course the density disparity remains, though aquatic respiration has the benefit of ram ventilation (i.e. moving through the medium absolves you of having to pump it). That'd might also imply she has both types of gills.
Additionally, we can't know if Waggy-Saggy has the same oxygen requirements as land dwellers. Even mammals can hold their breath for multiple hours by dialling back their metabolism, and since she canonically overwinters beneath the frozen lake, she likely can do with less.
No, the important question is: does her lung function as swim bladder? They're homologous, after all. But that probably means she can't speak or give underwater kisses whilst diving. Sad, science ruined another fantasy.