Answer:
This time next month I won't be in a crowded office, I'll be lying on a beach in Greece.
Step-by-step explanation:
The given sentence is in the future continuous tense. This is evident by the use of "this time next month", which suggests what is to happen in the future. Though the use of "this time" may suggest a present scenario, the adjoining phrase "next month" presents a future tense.
So, the correct words to be used in the given blank will be "I'll be lying", in the future "will+be" form".
Thus, the correct answer is the second option.