The lasix did not cause the respiratory arrest, they just happened to be next to each other chronologically. Likely she had pulmonary congestion (CHF) on top of the above problems. Even if she didn't, lasix is a pretty standard treatment for breathing problems because it is a quick fix for a probable problem. The respiratory failure was likely more related to her underlying COPD.
What likely happened:
1) Pneumonia tends to start in the bases of the lungs and work upwards, think gravity. Unfortunately, the bases of the lungs are also where most of the actual respiration (VQ matching, perfusion) occurs..with some occuring in the mid lung and almost none happening in the apex. So, her ability to oxygenate was compromised.
2) This was exacerbated by her COPD. Either she has chronic bronchitis (and can't get enough air into the lungs anways) or she has emphysema (and can't get air out of the lungs).
3) These two things add together to create a big problem with lung perfusion and blood oxygenation. As her blood O2 drops, CO2 starts to rise creating an acidotic state. Hyperventilation occurs to blow off the CO2 (compensatory) but this only makes the problem worse for her..the faster breathing does no good because she's not getting enough air into the lungs to make a difference and isn't holding the air long enough to recruit the collapsing alveoli. Blood CO2 continues to rise, pH continues to fall. Eventually the body can no longer compensate and the lack of O2 and increasing acidosis starts to produce changes in mental status. At a certain point, respiratory arrest occurs. When the arrest will occur is different person to person, but on a long enough timeline with these problems, compensation is less likely than arrest. Had she only had pneumonia and no underlying COPD and CHF, she likely could have compensated with tachypnea alone..but the comorbid lung issues made compensating impossible.
As for the arrest being the reason she's still in the hospital, maybe..maybe not. Is she still intubated? Then yes. If not, then it's because of the pneumonia and they are waiting on resolution of the pneumonia before they transfer/discharge...because if they discharge her with pneumonia and pulmonary congestion that is unresolved..she'll be back.
Hope this helps!