Paul was declaring to them that the time of the Day of the Lord, the man of lawlessness, and the apostasy had not yet come, as some were claiming. Paul informs them in vv. 3ff. that it was still future. He makes no claim or hint that it will be in their lifetimes, but only "at the proper time" (2 Thes. 2.6).

Where do you see in the text that he was expecting apostasy in his time period?

A.T. Robertson writes,[quote]"The Second Coming not only is not imminent, but it will not take place before certain important events take place, a definite rebuff to the false enthusiasts of v. 2. Paul speaks here of a religious revolt against truth. It is unclear whether Paul means revolt of the Jews from God, of Gentiles from God, of Christians from God, or of the apostasy that includes all classes within and without the body of Christians. But it will happen before Christ returns."[/quote]

Paul was expecting apostasy in his time period. So why apostasy hasn't came yet?

Paul wrote to Thessalonians who became lethargic that day of Lord hasn't yet started and will not come until an apostasy comes first & man of lawlessness be revealed.

So we can safely say that they were expecting apostasy in their own time period.