The correct answer is D. To desert someone in his difficulties.
To leave someone in the lurch means to abandon them or leave them in a difficult or embarrassing situation. It is often used in the context of friends or family members who have let each other down. For example, if you are supposed to meet a friend for dinner and they don’t show up, you might say that they have left you in the lurch.
The other options are not correct. Option A, to come to compromise with someone, means to reach an agreement by making concessions on both sides. Option B, to be a constant source of annoyance to someone, means to be someone who is always getting on someone’s nerves. Option C, to put someone at ease, means to make someone feel comfortable or relaxed.
I hope this helps!