The correct option is B will have lived
Here, 'will have lived' is correct because 'will have', in future perfect tense, is used to indicate an action that will be complete before another takes place. Here, by 2099, Turks will have lived in Anatolia for a thousand years.
'Will be', in future continuous tense, is used to indicate what will be going on at some time in the future. Example: I will be going to Delhi tomorrow.
'Have lived', in present perfect tense, is used to indicate past action which is not defined by a time of occurence.
'Will live', in future simple tense, is used to indicate an action that has not taken place as yet. Example: I will eat a burger tomorrow.