When she later stood him up, he sought her out at home and she warned him of what was to come for her, that she had a year or less to live. He dismissed her concerns as unimportant, because he'll be there for her if she'll have him, and she can either spend the time she has left dying, or living...with him. He presented her with two airline tickets to anywhere, 'everywhere if there's time.'
The two start on Alexa's world tour with the 'Tour of the New World,' a cross country trip, to be followed by trips to among other places, Egypt, Israel and Greece. She particularly loved Santorini, but three weeks after their visit there, her illness took a turn for the worst, and she entered hospital in Geneva.
Methos only left her side briefly on two occasions during their time together, once when Duncan MacLeod suffered a Dark Quickening and needed help, and once, after Alexa was put on life support in Geneva, he left her to attempt to find the Methuselah Stone in a desperate bid to save her life. The Stone was lost, however, and Methos hurried back to the Sacré Coeur Hospital in Geneva to find Alexa near death. He annointed her with myrrh, and climbed into the bed with her, where he held her throughout their last hours together.
He consider taking Alexa's body back to Santorini because she loved it there, but he didn't want her to be so far away, so returned to Paris and had her buried Montparnasse cemetery under the epitaph: Beloved.
She appeared in Highlander: The Series episode Timeless and in the short story collection Evening at Joe's. She was also mentioned in the video, Highlander: Reunion, which took place years after her death, wherin Methos had thought he would never feel again what he'd felt for Alexa, but was then contemplating marriage to a mortal woman, Julia.
Note: For details on Alexa's life and death with Methos see Postcards from Alexa.