If deep space is shown as it was in the past how can we calculate this time lagging regarding the Hubble parameter which is a variable of time?
The Hubble parameter does vary with time, in a way that depends on the cosmological parameters or the adopted cosmological model.
Observations of the redshifts of objects at known distances, over a broad range of distances, samples the expansion history of the universe over the time it takes for the light to reach us from the most distant objects in the sample.
It is exactly this type of measurement, using type Ia supernovae, that has led to the conclusion that the expansion of the universe was decelerating, but then began to accelerate from about 6 billion years in the past onwards.
Having established what the cosmological parameters are, then our cosmological model tells us what the Hubble parameter was at any cosmic epoch, but actually you can view the whole process as modelling the variation of the Hubble parameter with time to yield the cosmological parameters.
A more technical discussion is here.