Character Analysis
"Oh, how the good die young," Gustave laments of his eighty-four year old lover. Madame Celine Villeneuve Desgoffe und Taxis' (or, you know, just Madame D.) passing shouldn't come as much of a surprise, though. She knew something bad was about to happen to her—the last time she visits the Grand Budapest she is, as Gustave so eloquently describes, "shaking like a shitting dog,"—er—"suffering a more acute attack [of travel anxiety] on this occasion."
The last time they meet, Gustave pretty much ignores her premonition that they might never meet again (unless you count Gustave flirting with her beautifully manicured corpse). He sends her off abruptly, and even lies when he says that he will personally light a candle in the sacristy of Santa Maria for her. However, despite his shortcomings, Gustave seems to actually love and comfort Madame D.—he doesn't prey upon her, as Dmitri suggests.
When Zero interrupts Gustave in a patron's hotel room, he says, "we must go to her at once," mostly ignoring the calls in French from whom we assume is another of his elderly lady lovers in the room. Madame D. isn't just another lady for Gustave. She is of prime importance—though how much of that is due to her sexual prowess is unclear.
In the end, we learn that Madame D. is actually the "mysterious proprietor" of the Grand Budapest. Gustave had been unknowingly entertaining and comforting the owner of his beloved establishment all those years.