What is the difference between have lived vs have been living. For example.
This August, I will have lived in Yemen for three years.
This August, I will have been living in Yemen for three years.
future prefect and future prefect continuous:
This August, I will have lived in Yemen for three years.
[tells us when the fact will be true in the future}
This August, I will have been living in Yemen for three years.
[emphasize the ongoing nature of the activity in the future]
simple tenses versus continuous tenses mostly convey this:
I am walking to school every day this week. [specific] I generally do not walk to school. [general]
Lambie's answer is good. I just want to add a little more info.
This August, I will have lived in Yemen for three years.
This first sentence has the nuance that the topic will be about those past three years living in Yemen, and (very subtly) not really about the future. Because of that, it almost sounds like the speaker will be moving away from Yemen after August, like they had some sort of three-year residence program that would be ending in August.
This August, I will have been living in Yemen for three years.
This has the nuance of something happening in the past, as well as the present and future. It sounds more like the speaker is commemorating a three-year anniversary of living in Yemen and looking forward to living there even longer.