People sometimes refer to data worth looking at as being rich.
With large data sets, you may wish to distinguish between the data that have useful meaning and the data that do not. In the sciences, the useful part of the data (the information) is often called the signal, while the non-useful part of the data is called the noise.
We can then refer to the signal to noise ratio. A rich dataset has a high signal to noise ratio, while a data set that is mostly garbage has a low signal to noise ratio.
As far as your direct question:
- large information from the data
I have never heard information described as "large."
- lots of information from the data
This could be fine - depending on the verb that comes before lots.
- There is [lots / a lot] of information in the data.
- I extracted [lots / a lot] of information from the data.
I think there is some reason to prefer [a lot of] over [lots of] but I can't remember why. Both expressions are very common.
- sufficient information from the data
Similar to a lot of, in that the choice of preposition depends on the verb.
Different in that sufficient means enough, and is not a synonym of lots.
- We don't know exactly how efficient this new car is, but I was able to extract sufficient information from the data to know that it is an improvement on the old design.