When an anxious recluse agrees to take his cancer-fighting friend on one last adventure, he doesn?t bank on having his beliefs, loyalties and survival skills challenged when she falls fatally ill.

Why is her invite and dare such a strongly motivator for the MC? It comes across as a weak inciting incident. What more a significant event can you give the MC?

When invited by a terminal cancer patient, an anxious online recluse dared to join her on a road trip, but when she falls fatally ill he is left responsible for getting her home.

Maybe slightly better?

"When a terminal cancer patient requests her friend, an online anxious recluse, to travel to the United States to join her on a road trip, he isn?t prepared to cope when she turns fatally ill."

The problem with this revision is that it doesn't clearly identify the main character. It starts from the perspective of the woman, and then changes to the man. All other characters should be described by their relationship to the protagonist. The logline also needs a specific destination or goal. What does the road trip accomplish? Where does she want to go, or what does she want to see?
What's the conflict of the story? I can't recognize any external conflict from either versions of the logline.
But anyway, here's an example:?After his friend turns fatally ill, an anxious recluse must take her on a road trip across the U.S so she can visit her grandmother.?
Just an example using elements from your concept. But again, what's the conflict, what's the point of the journey?