The hospital scene
Why did Lidia cry? Was she upset by the fact that Tommaso was going to die or her marriage was falling apart?
What was up with the sick girl in the other room? Was she mentally ill or normal but hadn't had a man for a long time?
Lidia was crying probably (apart from the script telling her to) because she realized the connection between the dying Tommaso (who represented the best moments in her husband's professional life) and her dying marriage. Besides this, it's likely that, as sometimes happens at a person's passing, his death provoked some feelings for him that had been latent for some time.
As far as the famous match scene outside the door of the hospital room, well...striking a match is always symbolic of the flame of passion. In Antonioni, nothing is rational at all...people act out of emotional emptiness, ennui, anomie.