Is the time lapse considered when estimating the age of the universe? We say that our universe is 13.7 billion years ago. During the big bang, it doubled at least 90 times in trillionth of a second (as given here), and other topological statements.

The question is which time are we talking about. Is the time-lapse considered? If yes, how?
As relativistic effects will cause clocks to run slower, a frame of reference must be chosen when considering the time of the "big bang". There is a natural and convenient choice of reference frame, based on the cosmic microwave background. The cosmic background appears to be extremely red-shifted light, indicating it is receding from us very fast, due to the expansion of the universe. If we choose a frame in which the CMB is receding equally fast in all directions, we have a convenient frame of reference. It is called the Comoving frame. 

Now that we have a frame of reference, we can talk about time and distance in a way that all observers that share this frame can agree. In the comoving frame, the "big bang" occurred about 13.8 billion years ago.

To directly answer the question: The time measured is the time in the comoving frame and relativistic time dialations (time-lapse) are considered.